three essays on supplementary health insurance

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Three essays on Supplementary Health InsuranceMathilde Péron

To cite this version:Mathilde Péron. Three essays on Supplementary Health Insurance. Economics and Finance. Univer-sité Paris sciences et lettres, 2017. English. �NNT : 2017PSLED015�. �tel-01586231�

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THÈSE DE DOCTORAT

de l’Université de recherche Paris Sciences et Lettres

PSL Research University

Préparée à l’Université Paris-Dauphine

COMPOSITION DU JURY :

Soutenue lepar

cole Doctorale de Dauphine — ED 543

Spécialité

Dirigée par

Three essays on Supplementary Health Insurance

20.03.2017Mathilde PÉRON

Brigitte DORMONT

PSL, Université Paris-Dauphine

M. Eric BONSANG


Mme Brigitte DORMONT

M. Andrew JONES

University of York

Mme Florence JUSOT


M. Mathias KIFMANN

Universität Hamburg

M. Erik SCHOKKAERT

KU Leuven

Sciences économiques

Membre du jury

Directrice de thèse

Membre du jury

Présidente du jury

Rapporteur

Rapporteur

L’UNIVERSITÉ PARIS-DAUPHINE n’entend donner aucune approbation ni improbation aux opinions

émises dans les thèses ; ces opinions doivent être considérées comme propres à leurs auteurs.

Remerciements ∼ Thanks

Pour écrire une thèse il faut trois choses : du travail, de la persévérance ... et du travail12. Pour dire

vrai, il faut bien plus que ça.

Pour écrire une thèse, il faut des gens qui vous inspirent et qui vous font confiance, qui posent un regard

juste et bienveillant sur vos balbutiements de bébé chercheur.

Brigitte, j’ai une dette incommensurable. Sache que je ne compte pas la rembourser. Cela me rendra à

jamais redevable, me rappellera ce que je te dois.

Many thanks to Eric Bonsang, Andrew Jones, Florence Jusot, Mathias Kifmann and Erik Schokkaert

for being members of the committee. Your research has been inspiring and I am extremely honored by

your presence.

Merci à tous ceux qui m’ont accompagnée, ont ouvert des voies, ont guidé mes choix. Merci à Eve Car-

oli, Sandrine Dufour-Kippelin, Carine Franc, Stéphane Gauthier, Agnès Gramain, Damien Heurtevent,

Hélène Huber, Marie-Eve Joël, Andrew Jones, Florence Jusot, Stéphane Le Bouler, Pierre Lévy, Jérôme

Minonzio, Anne-Laure Samson, Estelle Suriray-Lemière, Alain Trannoy, Jérôme Wittwer. Je remercie

tout particulièrement Marc Fleurbaey pour cette aventure de 10 mois à Princeton.

Je remercie la Chaire Santé, le Labex Louis Bachelier, l’Académie Française ainsi que la fondation

Fulbright pour leur soutien financier. Merci à la MGEN et tout particulièrement à Jean-Louis Davet,

Dominique Furstein, Mylène Limbe, Nathalie Locufier, Constance Pillet et Nathalie Voisin.

Pour écrire une thèse, il faut aussi des mamans, des potes de Crous, de bureaux, de hand, de campus

américain et de ukulele. Et puis bien évidemment des gentils parents et une petite Pupu.

1d’après mon Papa, qui tient cela de Rocky, le coq volant dans Chicken Run2si j’ai dit deux fois travail c’est qu’il faut deux fois plus de travail que de persévérance

Les mamans ça vous apprend plein de trucs, ça vous emmène en ballade, vous ramène à la maison quand

la péniche tangue trop fort. De près ou de loin, elles gardent toujours un oeil sur vous. Moi j’ai la chance

d’en avoir cinq ou six des mamans... Et quand je serai grande, je ferai tout comme elles. Fanny, Cham,

Aurore Schilte, Blan, Emilie... voilà, l’Enfant a enfin fini ses devoirs... Je peux aller jouer maintenant ?

Les potes de Crous c’est tout aussi important pour la thèse et dans la vie en général. C’est vital même.

Pas seulement parce que vous mangez de la purée et de la? ... viande? Ah d’accord3 ...avec eux. Aussi

parce que les potes de Crous vous comprennent, vous soutiennent, réfléchissent ensemble à pouquoi α

est tour à tour positif et négatif. Ils disent des trucs rigolos, débrieffent le dernier Faites entrer l’accusé,

mangent des bonbons qui piquent à cinq heures le vendredi. Le meilleur c’est qu’entre potes du Crous,

on n’a même plus besoin d’aller au Crous, on est juste potes. On se reconnaît où qu’on soit. Louis,

Romain, Mathilde, Nina, Lexane, Nico, Clémentine, Ludivine, Amine, Éléonore ... Merci les amis.

Il y a aussi les potes de bureaux, Sandra, Karine, Geoffrey, Marine, Yeganeh, Fatma, Manuel, Fayçal,

Victoria, Catherine. Ceux avec qui on discute d’abord entre deux portes du temps, du plan de réamé-

nagement du territoire, du dernier corrigé de macro et puis qui eux aussi deviennent des amis. Merci aux

"anciens", Cécile, Caro et Damien pour les coups de pouce du début. Je pense aussi bien sûr Aurélia,

copine de Master. Aux potes du Cermes, Magali, Jonathan, Clémence P, Clémence B, loin tout là-bas

à Villejuif et qui montaient à la capitale pour les fameuses Cermes-Legos parties. Aux amis des jeudis

matins à la MSE, Marlène, Léontine et Robin.

Et puis il y a tous les autres potes. Ceux qui au départ n’ont strictement rien à voir avec cette satanée

thèse mais comme vous les bassinez avec depuis 5 ans, 6 mois et 20 jours, ben ils font malgré eux partie

de l’aventure. Alors en mettant un point final à tout ça, j’ai une petite pensée pour tous les amis du PSC,

pour ma coloc Lucie, pour Mendyne, pour Vivien. Thanks to my dear Princetonian friends Thomas,

Vanessa, Elena, Scott, Alex, Enrico and the Italian gang. I also have a tender and thankful thought for

Jürgen. Many thanks to my UKe buddies Will, Dan and Derek. You’re a rainbow in my clouds.

Merci enfin à mes parents. Pour les Loto-fleurs, les histoires le soir, les dictées de pré-rentrée, les tours

de vélo, le riz-t-au-lait. Pour leur amour, leurs inquiétudes, leur soutien inconditionnel et la confiance

qu’ils ont mise à l’intérieur de moi. Big Up à la petite Pupu, que j’aime tellement fort.

Que je le veuille ou non cette thèse est une partie de moi. Moi qui ne suis rien sans vous. Alors que vous

le vouliez ou non tout ce qui ce trouve là, tout ce qui va suivre, est en partie à cause de vous, entièrement

grâce à vous. Mathilde.

3...et des Jockeyr gratos

vi

Contents

General Introduction 1

Résumé 29

Prelude 37

1 Does health insurance encourage the rise in medical prices? A test on balance billing

in France 47

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

1.2 Insurance coverage, medical prices and balance billing: results from the literature . . . . 51

1.3 French regulation of ambulatory care and balance billing . . . . . . . . . . . . . . . . . . 52

1.3.1 The decision to consult a Sector 2 specialist . . . . . . . . . . . . . . . . . . . . . 53

1.3.2 Availability of Sector 1 and Sector 2 specialists . . . . . . . . . . . . . . . . . . . 55

1.4 Data and empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

1.4.1 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

1.4.2 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

1.4.3 Basic features of the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

1.5 Econometric specification and estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

1.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

1.6.1 The impact of better coverage on the use of Sector 2 specialists and balance billing 63

1.6.2 The effect of supply side organization on the impact of better coverage . . . . . . 64

1.6.3 Other determinants of balance billing . . . . . . . . . . . . . . . . . . . . . . . . . 65

1.6.4 Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

x Contents

2 Selection on moral hazard in Supplementary Health Insurance 79

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

2.2 Method: Marginal Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

2.2.1 The Generalized Roy model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

2.2.2 Marginal Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

2.2.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

2.3 Data and empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

2.3.1 Basic features of the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

2.4 Empirical specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

2.4.1 Model and estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

2.4.2 Interpretation of the estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

2.5.1 Influence of observable characteristics: consumption of balance billing without

coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

2.5.2 Influence of observable characteristics: demand for better coverage . . . . . . . . 101

2.5.3 Influence of observable characteristics: moral hazard . . . . . . . . . . . . . . . . 101

2.5.4 Influence of observable characteristics: classical adverse selection and selection

on moral hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

2.5.5 Heterogeneity in moral hazard depending on unobservable characteristics . . . . . 102

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


3 Supplementary Health Insurance: are age-based premiums fair? 117

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

3.1.1 Aim of the paper, methodological framework and contributions . . . . . . . . . . 120

3.2 How to define and design fair healthcare payments? . . . . . . . . . . . . . . . . . . . . . 125

3.2.1 Healthcare payments: concepts and definitions . . . . . . . . . . . . . . . . . . . 125

3.2.2 Literature: efficiency and fairness of healthcare payments . . . . . . . . . . . . . 127

3.3 Measuring the extent of risk sharing and vertical equity . . . . . . . . . . . . . . . . . . . 134

3.3.1 Vertical equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3.3.2 Risk sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

3.4 Decision to take out SHI, premiums and market’s dynamic . . . . . . . . . . . . . . . . . 136

3.4.1 Health insurance premiums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

3.4.2 Individuals’ decision to take out SHI . . . . . . . . . . . . . . . . . . . . . . . . . 138

Contents xi

3.4.3 Market’s dynamic when insurance is voluntary . . . . . . . . . . . . . . . . . . . 139

3.5 Empirical application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

3.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

3.5.2 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

3.5.3 Calibration and computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

3.6.1 Consequences of voluntary SHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

3.6.2 Age-based premiums and vertical equity . . . . . . . . . . . . . . . . . . . . . . . 147

3.6.3 Age-based premiums and risk sharing . . . . . . . . . . . . . . . . . . . . . . . . . 148

3.6.4 Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

3.6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154


Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

A-3.1. Equity indexes: formulas and computation . . . . . . . . . . . . . . . . . . . . . . 176

A-3.2. Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

General Conclusion 183

Bibliography 193

List of Figures

1 Financing health care: international comparison . . . . . . . . . . . . . . . . . . . . . . 42

2 Average coverage by type of care in France in 2014 . . . . . . . . . . . . . . . . . . . . 42

3 SHI coverage in France in 2014: type of contracts by occupation . . . . . . . . . . . . . 43

4 SHI coverage in France in 2014: type of contracts by income groups . . . . . . . . . . . 43

5 Number of firms on the French health insurance market, 2001-2014 . . . . . . . . . . . 44

6 Market shares on the French health insurance market, 2001-2014 . . . . . . . . . . . . 44

1.1 Specialist:population ratio at the département level for Sector 1 and Sector 2 specialists

in 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

1.2 Share of consultations of Sector 2 specialist (Q2/Q) and average balance billing per

Sector 2 consultation (BB/Q2) in 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

1.3 Control and treatment groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

1.4 Number of MGEN enrollees who retired in 2010, 2011 and 2012, by age . . . . . . . . . 74

2.1 Treatment choice for given propensity score P (Z) and values of disutility UD . . . . . . 106

2.2 Common support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

2.3 Parametric MTE - log(Q), log(Q2/Q), log(BB/Q), BB/Q, log(BB/Q2) . . . . . . . . 113

2.4 Semi-parametric MTE - log(Q), log(Q2/Q), log(BB/Q), BB/Q, log(BB/Q2) . . . . . 114

2.5 Empirical ATE on log(BB/Q) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

3.1 Income, healthcare payments and vertical equity . . . . . . . . . . . . . . . . . . . . . . 157

3.2 Supplementary healthcare expenditures, payments and risk sharing . . . . . . . . . . . 158

3.3 Distribution of supplementary healthcare expenditures (SHE), SHI reimbursements

(SHIR) and out-of-pocket payments(OOP ), MGEN sample 2012 . . . . . . . . . . . . 161

3.4 Distribution of income and concentration curves for supplementary healthcare expen-

ditures (SHE), SHI reimbursements (SHIR) and out-of-pocket payments (OOP ),

MGEN sample 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

xiv List of Figures

3.5 Distribution of SHI reimbursements by age, MGEN sample 2012 . . . . . . . . . . . . . 163

3.6 Empirical distribution function of supplementary healthcare expenditures (SHE), by

risk groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

3.7 Healthcare payments and vertical equity . . . . . . . . . . . . . . . . . . . . . . . . . . 171

3.8 Healthcare payments and risk sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

3.9 Stata code - vertical equity indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

3.10 Stata code - risk sharing indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

3.11 Macro for computing expected utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

3.12 Macro for simulating adverse selection with uniform premiums . . . . . . . . . . . . . . 182

List of Tables

1 Average coverage in euros, by age-group, in 2013 . . . . . . . . . . . . . . . . . . . . . . 45

1.1 Number of Stayers and Switchers and individual characteristics in 2010 . . . . . . . . . 70

1.2 Number of specialist visits and amount of balance billing in euros in 2010 . . . . . . . 71

1.3 Impact of better coverage on visits to a specialist, use of Sector 2 specialists and average

amounts of balance billing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

1.4 Effect of demand and supply side drivers on visits to a specialist, use of Sector 2

specialists and average amounts of balance billing . . . . . . . . . . . . . . . . . . . . . 73

1.5 Characteristics of "early retirees" and "movers" in 2010 (Probit estimations) . . . . . . 75

1.6 Impact of better coverage and chronic disease onset on GP visits and drugs consumption

(Whole sample) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

1.7 Instruments: First stage coefficients and F-stat . . . . . . . . . . . . . . . . . . . . . . 76

1.8 Robustness check: impact of better coverage when using "early retirees" as the only

excluded instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

1.9 Robustness check: impact of better coverage on different categories of SPR1 (2SLS) . . 77

2.1 Number of MGEN-SHI and better-SHI holders and individual characteristics in 2012

for individuals with at least one visit to a specialist (Q ≥ 1) . . . . . . . . . . . . . . . 107

2.2 Number of specialist visits and amount of balance billing in e in 2010 and 2012 for

individuals with at least one visit to a specialist (Q ≥ 1) in 2010 and 2012 . . . . . . . 107

2.3 Effect of covariates and excluded instruments on the probability of taking out better

coverage (PROBIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

2.4 Effect of covariates on the consumption of balance billing and on moral hazard . . . . . 110

2.5 Obervables: summary of relationships between probability of switching, demand for S2

specialists without coverage and moral hazard - average balance billing per consultation

(BB/Q) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

2.6 Polynomial coefficients and joint test of significance . . . . . . . . . . . . . . . . . . . . 111

xvi List of Tables

2.7 Capturing Moral hazard and the effect of unobservables: OLS, IV, empirical ATE and

semi-parametric MTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.1 Socio-demographic characteristics - MGEN sample, 2012 . . . . . . . . . . . . . . . . . 159

3.2 Empirical mean, standard deviation and percentiles of supplementary healthcare ex-

penditures (SHE), SHI reimbursements (SHIR) and out-of-pocket payments(OOP ),

in e, MGEN sample in 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

3.3 Correlation between SHI reimbursements (SHIR) and age . . . . . . . . . . . . . . . . 163

3.4 Predicted supplementary health care expenditures (SHE) and SHI reimbursements

(SHIR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

3.5 Empirical mean, standard deviation and percentiles of supplementary healthcare ex-

penditures (SHE) by risk groups λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

3.6 Empirical mean, standard deviation and percentiles of OOP payments by risk groups λ 165

3.7 Adverse-selection spiral when insurance is voluntary: effect on premiums, results from

simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

3.8 Characteristics of insured and uninsured when SHI is voluntary, results from simulations168

3.9 Percentage of uninsured by income and risk profile, for each regime of premiums -

results from simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

3.10 Vertical equity indexes, results from simulation - whole sample . . . . . . . . . . . . . . 170

3.11 Risk sharing indexes, results from simulation - whole sample . . . . . . . . . . . . . . . 172

3.12 Vertical equity and Risk sharing indexes, results from simulation - SHIR only - Volun-

tary whole sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

3.13 Different values of load factor and risk aversion - Voluntary whole sample . . . . . . . . 175

General Introduction

Health insurance plays a central role in funding medical care. It protects people against catas-

trophic medical expenditures that they could not afford without insurance coverage. Health

insurance also contributes to reduce medical expenditures’ impact on individuals’ budget and

mitigates the vicious circle between income and health when poor health results in poverty, and

access to care is limited by income.

Designed to favor access to care, social health insurance systems ensure minimal coverage for

a large proportion of the population and are widespread among developed countries. However,

because of greater use of medical services and technology changes, healthcare expenditures grow

faster than nations’ GDP and put public finances under severe strain. Rather than increasing

contributions, the chosen option is often to limit the perimeter of coverage either in terms of

population, price or type of medical goods and services covered. This creates space for the

development of a market where individuals can buy supplementary health insurance to enhance

their coverage. A private market providing supplementary coverage is a mixed blessing. On

the one hand, it releases public constraints, allows people to opt for the plan that is best for

them and gives insurers incentives to increase efficiency and quality. On the other hand, sup-

plementary insurance might creates difficulties as regards efficiency of the healthcare system as

a whole and fairness in access to care. First, if individuals increase their consumption in terms

of quantity and/or quality due to a better coverage, supplementary insurance can contribute

to the exponential growth of healthcare expenditures. The fact that supplementary coverage is

voluntary can worsen the inflationary effect if those who decide to buy insurance are actually

those who get the most from it and increase more sharply their demand for healthcare. Second,

contrary to most common goods, like cars or computers, health insurance price can depend on

2 General Introduction

individuals’ characteristics, especially their age, gender or health status. Competition also leads

insurers to select individuals with lower expected healthcare expenditures. Consequently, pro-

viding supplementary insurance in a competitive market is likely to result in strong inequalities

in the extent and the price paid for coverage and eventually the price paid for healthcare.

This thesis deals with questions regarding efficiency and fairness in mixed health insurance

systems with partial mandatory coverage and voluntary supplementary health insurance. We

focus on the potential inflationary effect of supplementary insurance on prices of medical services

that are jointly covered by both mandatory and supplementary insurance. We also question,

from the patient perspective, the fairness of supplementary insurance premiums when supple-

mentary health insurance is voluntary. We adopt an empirical approach and set our analysis

in the French context where mandatory insurance is universal yet partial and individuals can

enhance their coverage by buying supplementary coverage in a competitive market. Our em-

pirical analysis is performed on original individual-level data, collected from the administrative

claims of a French insurer (Mutuelle Générale de l’Éducation Nationale, MGEN). The sample

is made of 99,878 individuals observed from 2010 to 2012. Contrary to existing data in France,

our database provides healthcare consumption and reimbursements from both mandatory and

supplementary coverage.

Our analysis focuses on the relationship between individuals and insurers; precisely on individ-

uals’ choice of coverage, healthcare use and the price of insurance contracts. We do not address

other issues raised by health insurance systems such as production of healthcare or relation-

ships between insurers and care providers (see Cutler & Zeckhauser (2000) for an overview).

As regards insurance design, we do not question the optimal size of public and private coverage

neither co-insurance optimality. Also, regulation issues on the health insurance market such as

the implementation of risk adjustment schemes are not examined in this thesis. Although our

results give insights on the role of supplementary insurance on access to care, we do not directly

estimate the effect of health insurance on health.

The general introduction is organized as follows. First, we characterize health insurance systems,

define important concepts and further discuss the inefficiencies and inequalities created by a

voluntary supplementary health insurance. We then present the main objectives of our thesis


and our methodology. Finally, we summarize the questions, methods and results of our three

chapters.

Health insurance triad: mandate, premiums and benefit package

Health insurance systems can appear as diverse and complex. We first discuss the distinction

between public and private insurance and then focus on three features of health insurance

schemes: whether insurance is mandatory or voluntary, the way premiums are defined and

finally the benefit package design.

Public, private and mixed health insurance systems

A classical taxonomy of health insurance would oppose public and private systems even if the

distinction is not always straightforward. Colombo & Tapay (2004) propose a classification

based on the source of funding; public insurance would refer to insurance schemes financed

through taxation or payroll contributions whilst private insurance would imply that insurance

schemes are financed through private premiums paid directly to the insurer. Consequently, sys-

tems where insurance is mandatory but provided by not-for-profit sickness funds or commercial

companies would be classified as private. Yet, Germany, the Netherlands or Switzerland have

adopted a form of ‘managed competition’, as defined by Enthoven (1993), where individuals

are free to choose their insurer, yet insurance remains mandatory, the standard benefit package

is standardized, premiums are uniform or income-based and insurers cannot refuse coverage.

Which, in the end, make these systems very similar to a public system funded by taxes or

payroll contributions. Furthermore, from the individual point of view, the way contributions to

insurance are collected, by the government, their employer or an insurance company, does not

really matter. We argue that what matters is whether insurance is mandatory or voluntary, to

which extent contributions depend on health risk or income and whether the benefit package is

standardized.

Because we do not adopt an institutional perspective but rather focus on the relationships be-

tween individuals and insurers, our description of health insurance schemes departs from the


taxonomy by Colombo & Tapay (2004). First, we do not distinguish between taxes, social

contributions and direct payments and rather use ‘premium’ as a generic term to refer to the

payment made by individual to be insured. We will discuss thoroughly health insurance pre-

miums’ definition further in this section. Second, we define as ‘public insurance’ insurance

schemes where insurance is mandatory, premiums are regulated, i.e. insurers cannot freely set

their prices, and the benefit package is standardized. Public insurance can be organized by a

single payer (French Sécurité sociale or Medicare in the USA), a public provider of healthcare

as in the UK, or through managed competition as in Germany, the Netherlands or Switzer-

land. By contrast, ‘private insurance’ refers to voluntary insurance provided on an unregulated

competitive market where insurers freely design their contracts in terms of prices and coverage.

In practice, systems where healthcare expenditures are only funded through public or private

insurance are rare, and the two sources of funding usually coexist in what is called a mixed

health insurance system.

In mixed systems where public insurance finances the main part of health expenditures, the

private health insurance market can assume different roles. It can be a substitute to public

coverage: individuals can opt out from the public scheme and purchase coverage on a private

health insurance market, as it is the case in Germany for high income groups and civil servants.

When public coverage is universal but partial, households can limit their out-of-pocket expenses

by contracting private health insurance. Mossialos & Thomson (2002) make a distinction be-

tween complementary and supplementary coverage. A complementary coverage is meant to

cover co-pays or goods and services not covered by public insurance whilst supplementary cov-

erage rather enhances patients’ choice and access to higher quality of care. We argue however

that most of private insurance contracts have both features and ultimately aim at increasing

coverage compared to mandatory basic insurance. We therefore choose not to distinguish in our

analysis between complementary and supplementary coverage. We also consider as supplemen-

tary coverage private insurance contracts that ‘duplicate’ public insurance (Colombo & Tapay

2004, Vera-Hernández 1999). In the UK, Spain, Italy or New-Zealand for instance, individuals

still have to contribute to public funding but they can buy private insurance to access higher

quality care and avoid waiting lists. In this specific case, public and private insurance are in

competition as regards basic healthcare coverage. This feature has important implications espe-


cially when one wants to estimate the impact of private coverage on public expenditures which

depends on whether individuals decide to use private insurance as a substitute or a comple-

ment. As regards our main questions however, we rather focus on the supplementary feature,

i.e. whether private insurance increases coverage compared to public insurance. To sum up,

when considering mixed health insurance systems with partial public coverage and voluntary

private insurance we use the term ‘National Health Insurance’ (NHI) to refer to basic coverage

(mandatory with regulated premiums and a standardized benefit package) and ‘Supplementary

Health Insurance’ (SHI) to refer to insurance contracts which complement and/or supplement

NHI coverage.

Mandatory vs. voluntary

When insurance is mandatory, individuals are enforced by law to contribute to the NHI scheme

and/or buy coverage on a private health insurance market. The mandate can be universal but

specific groups can also be allowed to opt out (high-income individuals for instance). It is worth

noting that the mandate can also concern employers by compelling them to provide health

insurance coverage to their employees. When insurance is voluntary individuals are free to buy

insurance or remain uninsured (and employers are free to provide coverage to their employees as

a fringe benefit). This does not necessarily mean however that policy makers are not concerned

by universal access to insurance. Vouchers for low-income individuals, tax exemptions or tax

penalties can be used as incentives to maximize coverage in the population even when insurance

is voluntary.

Health insurance premiums

As stated previously, we define a health insurance premium as a payment made by an individual

(either because it is mandatory or voluntary) to an insurer (either public or private) in order to

be covered against healthcare expenditures. The payment is made ex ante, i.e. before individuals

actually use healthcare. In this respect it differs from ex post payments that directly depend

on healthcare consumption such as out-of-pocket expenditures. It is worth noting that here,

ex ante and ex post respectively refer to before and after healthcare use rather than before

and after the realization of a health risk. This approach may not be conventional regarding the


theoretical literature on insurance but is meant to be more pragmatic. Indeed, an individual can

be diagnosed with cancer (the health risk is realized) but her use of healthcare is still uncertain

and, from this perspective, the premium remains an ex ante payment. A consequence of making

an ex ante payment is that the individual does not bear her own risk of having healthcare

expenditures but shares it with others. By paying a premium, the individual joins a ‘pool’ and

agrees that her contribution will be used to finance the pool’s healthcare expenditures. As a

matter of fact, health insurance always implies a form of ex post redistribution, e.g. low users

of medical care will subsidize high users. Health insurance therefore differs from ‘self-insurance’

for which healthcare expenditures are financed through saving or borrowing.

However, the extent of risk sharing can dramatically vary depending on how premiums are de-

fined and especially to which extent premiums are disconnected from individual characteristics.

Two practices are commonly opposed: ‘community rating’ and ‘actuarial fairness’. Community

rating (CR) implies that premiums are disconnected from the individual’s own risk. On the

contrary, actuarial fairness requires insurers to use all information available at the individual

level to predict the individual’s expected healthcare expenditures. However, in between those

two principles, one can draw a continuum of premiums, based on a decreasing risk sharing from

CR to actuarial fairness. The purest form of CR would be a uniform premium. A uniform pre-

mium is a flat fee, i.e. an equal contribution in absolute terms, paid by individuals regardless

of their own risk. The premium therefore depends on the expected average expenditures of the

whole pool and risk sharing is maximized. Further on the continuum, ‘adjusted community rat-

ing’ basically establishes a uniform premium among a restricted pool of individuals who share

characteristics that define their risk profile: age, gender, location and so on. However, as soon

as the criteria used to adjust for risk become more and more precise, the pool shrinks and risk

sharing is reduced. The way premiums are defined is then getting closer to actuarial fairness

principles. Indeed, besides socio-demographic characteristics, insurers will use all information

available to estimate individuals’ risk, especially current and previous health state (known as

‘medical underwriting’) or healthcare expenditures from the previous years (‘experience rating’).

Contributions based on income stand apart from this continuum because income is not used by

insurers to set premiums closer to individual risk. Motivations are related to concerns about


how premiums weight on individuals’ income. When insurance is mandatory, a premium discon-

nected from income would make the poor contribute relatively more than the rich (‘regressive

payments’). When insurance is voluntary, the possibility that the poor remain uninsured and

restrain their use of healthcare is an additional concern. It is important to note that even if

income-based premiums are widespread in European social health insurance systems, they are

not necessarily associated with public insurance (the Swiss system is financed through adjusted

CR) nor antagonist with private health insurance (in France, several not-for-profit health insur-

ers still make premiums depend on income). In mixed health insurance systems, an individual

can pay different premiums. In France for instance, individuals contribute to public insur-

ance with income-based premiums but purchase voluntary SHI with premiums which generally

increase with age.

In practice, the way premiums are defined can be influenced by various factors. First, regulation

can limit insurers’ ability to freely set their prices. For instance in the EU, anti-discrimination

laws ban gender-based premiums; in the USA, the Affordable Care Act bans medical underwrit-

ing. Second, premiums can reflect insurers’ strategies or ethical principles. However, two main

features of the health insurance scheme strongly influence how insurers define their premiums:

whether insurance is mandatory or voluntary and the intensity of competition between insurers.

It is difficult for an insurer to set premiums under CR principles when the competition attracts

low-risk individuals with premiums adjusted on individual risk. The mutuelles in France as

well as the Blue Cross and Blue Shield in the USA used to set uniform premiums mainly for

ethical reasons but the intensification of the competition in the individual market have almost

condemned pure CR.

Benefit package design

The extent of risk sharing in health insurance also depends on the extent of coverage, i.e the

perimeter of the ‘benefit package’. The benefit package is a three dimensions concept which

includes (i) the list of medical goods and services covered, (ii) the population covered (‘universal’

or ‘specific’) and (iii) the extent of coverage in terms of reimbursed costs (‘complete’ or ‘partial’).

The list of medical goods and services included in the benefit package as well as criteria used

to justify their coverage can be more or less explicit. Whether it concerns the whole package or


a specific treatment, coverage can also be conditional on individual characteristics such as age,

health state or income. For instance, the Medicare program in the USA only covers individuals

over 65, whereas the Medicaid program mainly covers very low-income individuals. Finally,

coverage can be universal yet partial, meaning that insurance reimbursements do not cover the

total cost of healthcare. These ‘co-payments’ between insurers and patients can take different

forms: a deductible on the total of expenditures meaning that insurance reimbursements only

start after a certain threshold; or, for a specific treatment a part of the cost, either expressed

as a fix amount or a percentage, is not reimbursed. These co-payments are directly borne

by patients and form ‘out-of-pocket’ (OOP) expenditures. OOP expenditures are simply the

difference between the total cost of healthcare and insurance reimbursements. In several health

insurance systems, especially in Germany and Switzerland, OOP expenditures are capped to

ensure that payments related to healthcare do not weight too much on households’ budget.

It is difficult to describe precisely the benefit package of a specific country, especially in mixed

health insurance systems. Indeed, a public benefit package usually coexists with a myriad of

private healthcare package depending on whether individuals are privately insured or not and

with which type of contract. Indeed, individuals can purchase SHI to upgrade the basic benefit

package either by getting coverage on co-payments or by adding medical goods and services

that are not covered at all by NHI.

Inefficiencies and inequalities in mixed health insurance systems

with voluntary SHI

Theoretically, mixed health insurance systems are supposed to take the best from both public

and private sides and reconcile equity and efficiency. A mandatory NHI ensures that individuals

have financial access to essential healthcare and that their contribution does not weight too much

on their available income. The private market, by offering voluntary supplementary coverage,

allows individuals to express their preferences. Moreover, competition in the private health

insurance market should guarantee productive efficiency by reducing costs and encouraging

innovations. Unfortunately, this ideal picture ignores the specificity of health insurance. In the

absence of a strict regulation, risk selection and moral hazard phenomena create inefficiencies


on both public and private sides and endanger the founding equity principles carried by social

health insurance systems.

Inefficiencies

Mixed health insurance systems suffer from two types of inefficiencies. The first source of

inefficiency is specific to the effect of risk selection in a competitive health insurance market

and has a strong impact on premiums and access to SHI. The second source of inefficiency comes

from moral hazard in a context where interactions between mandatory NHI and voluntary SHI

are likely to create an increase in medical prices.

Increasing premiums and partial coverage: the adverse selection phenomenon

The health insurance market is subject to self-selection with individuals choosing the contract

that maximizes their utility. For the same level of risk aversion, ‘low risk’ individuals, who expect

rather low medical care expenses, should have a lower willingness to pay for insurance contracts

than ‘high risk’ individuals. In a theoretical framework with perfect information, insurers

are able to separate low risk from high risk individuals and price their contracts with actuarial

premiums which depend on individuals’ expected expenditures. This would guarantee allocative

efficiency in the market with coverage choices driven by individuals’ willingness to pay. In reality,

the insurance market suffers from asymmetric information that yields adverse selection (Akerlof

1970). Individuals know their own risk but this information is private. Therefore, insurers

are only able to price their contract with a uniform premium based on the pool’s average

expenses and have to take into account strategic behaviors. If complete coverage is available

with a premium based on low risk’s expected expenditures, high risk will also buy insurance

and insurers will lose money. On the contrary, if premiums are based on high risk’ expected

expenditures, low risk will not buy insurance. Rothschild & Stiglitz (1976) demonstrate that,

when individuals have a better knowledge of their risk than insurers, low risk are only partially

covered and the market equilibrium is Pareto dominated.

However, because they have access to rich data and complex statistical models, insurers are

likely to have more accurate information on individuals’ risk than individuals themselves. When


asymmetric information benefits to insurers, Henriet & Rochet (1999) show that they can use

their knowledge to offer contracts that attract low risk at the expense of high risk either by

lowering premiums or segmenting contracts. Cutler et al. (1997) reach the same conclusion by

considering the dynamic consequences of adverse selection. To maximize profit, insurers offer a

set of contracts with different levels of coverage. Adverse selection, as described by Rothschild

and Stiglitz yields low risk to buy partial coverage (plan P) whilst high risk remain with complete

coverage (plan C). Yet, the equilibrium is unstable. If the premium gap is significant between

plans P and C, individuals with the lowest risk among plan C will join plan P to benefit from

lower premiums. Because of this loss, the pool’s average expenses in plan C will increase, driving

up premiums too. The premium gap between the two contracts keeps on enlarging and speeds

up the loss of individuals with lower risk from complete to partial coverage. Eventually, this

‘death spiral’ condemns comprehensive plans and yields partial coverage for individuals with

high medical expenditures.

Increasing medical prices: supplementary health insurance and moral hazard

The second source of inefficiency is peculiar to mixed health insurance systems. The economic

rationale for partial mandatory coverage is to contain moral hazard. Indeed, health insurance

lowers the price of medical care faced by patients. Assuming that demand for medical goods

decreases with prices, individuals are likely to increase their consumption. According to Pauly

(1968), this over-consumption is inefficient because the social marginal cost of healthcare exceeds

individuals’ marginal utility. The dynamic consequences of moral hazard also yield inefficiencies

by increasing medical prices and eventually insurance premiums (Feldstein 1970, 1973, Sloan

1982, Chiu 1997, Vaithianathan 2006). Blomqvist & Johansson (1997) therefore conclude that

a mixed health insurance system is less efficient than an unregulated competitive market or a

NHI. There is however an alternative interpretation of moral hazard by Nyman (1999). Nyman

considers moral hazard not only as a pure price effect but also as an income effect which traduce

better access to care. Thanks to insurance, which can be interpreted as an income transfer

conditional on the use of healthcare, individuals can have access to medical goods that were

otherwise unreachable considering their budget constraint. Non-desirable price effects must

therefore be balanced with desirable income effects that enhance social welfare by improving


healthcare access. Yet, regardless of how we interpret moral hazard, a mixed system loses on

both sides. On the one hand, if moral hazard has to be contained, supplementary coverage would

cancel out the effect of co-payments and be responsible for over-consumption and inflationary

spirals on prices and premiums. On the other hand, if the increase in medical care consumption

is desirable because it means better access to care, then co-payments cannot be justified by

any economic rationale especially if voluntary supplementary coverage only benefits rich and

healthy individuals who had already access to care anyway.

Indeed, voluntary supplementary coverage necessarily implies some self-selection phenomena

likely to worsen inefficiencies. Pauly (2000) investigates the American Medigap market, where

private insurers provide supplementary coverage for individuals over 65 who benefit from par-

tial coverage with Medicare; the Medicare/Medigap system is in this respect very similar to

the French system. Pauly notes that not only rich individuals are more likely to buy SHI, they

are also more likely to consume medical goods in higher quantity and quality. Moreover, inef-

ficiencies can also arise from a phenomenon of ‘selection on moral hazard’ in the SHI market.

Indeed, independently of income, expected expenditures or risk aversion, Einav et al. (2013)

show that individuals who are very sensitive to prices and therefore more likely to increase their

consumption once they are insured, are also more likely to ask for comprehensive coverage. As a

result, they drive up healthcare prices and SHI premiums. This eventually results in an increase

in OOP expenses for individuals without coverage and makes SHI even more essential but also

less affordable for low income and/or sick individuals.

Seminal contributions by Arrow (1963), Pauly (1968), Phelps & Newhouse (1974), Manning

et al. (1987), Nyman (2003) have extensively analyzed the moral hazard phenomenon. Yet, it

benefits from a renewed interest in the context of voluntary SHI. First, moral hazard can concern

both the quantity and the quality of medical goods. Second, it creates spill-over effects on the

public system which also bears the increase in medical prices. Finally, moral hazard is likely

to be heterogeneous among individuals and related to selection phenomena when insurance is

voluntary. Therefore, it is critical to open the moral hazard ‘black-box’ to understand the effect

of SHI on medical prices and access to care.


Inequalities in SHI coverage

A voluntary SHI, provided by insurers who compete on an unregulated market, creates in-

equalities in terms of access, coverage and premiums paid. These inequalities can be related to

individuals’ income, occupation, gender, age or health state and are likely to be cumulative.

In France, the proportion of individuals covered by SHI significantly increases with income.

Despite public programs targeting low-income population, 14.3% of individuals with a monthly

income below e650 declared to be uninsured in 2014. They were only 1.6% with a monthly in-

come above e2000 (DREES 2016). Similar pro-rich inequalities in SHI access have been stressed

out in Switzerland (Dormont et al. 2009), in the UK (Jones et al. 2006), in Belgium (Schokkaert

et al. 2010) as well as on the Medigap market in the USA (Fang et al. 2008). There are mainly

three reasons for these inequalities. The first reason is specific to France where employees with

a permanent and full-time job have an easier access to SHI through subsidized employer-based

contracts. Note that, on top of unequal access to SHI in terms of income, this situation also

enlarges the gap between ‘insiders’ and ‘outsiders’. Insiders, integrated to the labour market,

probably wealthier and healthier, have an easier access to insurance coverage whereas outsiders

– students, unemployed and pensioners – likely to have tighter budget constraints and/or higher

medical needs have to buy insurance on the individual SHI market. Second, in the individual

market, premiums rarely depend on income which makes payments regressive: the share of

income dedicated to SHI premium can represent only 2.9% of the wealthiest households but up

to 10.3% for the poorest (Kambia-Chopin et al. 2008). Finally, independently of affordability

concerns, the willingness to pay for SHI possibly increases with income. At first glance, this

seems contradictory with a commonly assumed decreasing risk aversion with income. However,

as noted by Dormont et al. (2009), SHI also includes coverage for high quality medical goods

(private room in hospital, shorter waiting lists or fancy glasses) for which high-income groups

are likely to have higher willingness to pay.

Inequalities in SHI access and premiums paid also arise when insurers use individuals’ charac-

teristics to price their contracts. For instance, age is a good predictor of medical expenditures

and age-based premiums are easy to implement. Insurers therefore offer contracts for which

premiums can vary with a ratio of 1 to 3 depending on age. This obviously creates inequalities


in terms of premiums paid between younger and older age groups and has immediate conse-

quences on access to SHI and level of coverage. According to a French survey conducted in

2013 (DREES 2016), among the 60+ age-group, 40% of SHI policyholders benefits from a very

basic supplementary coverage (co-payments only, no balance billing coverage and limited cover-

age on dental and optical care) versus 29% among the 25-59 age group. On average, individuals

over 60 are also less covered on every type of medical care: the average coverage for specialist

consultations is e13, versus e18 for the 25-59 age-group; coverage for complex optical devices

is also 20% lower for the 60+ age-group compared to the 25-59. Residential location, family

composition, gender or medical history can also be used to price contracts leading to the same

kind of inequalities.

As stated previously, selection phenomena can also yield inequalities in coverage related to

individuals’ health state. It is worth noting that theoretical predictions about adverse selection

in insurance – e.g. higher risk individuals should seek for more comprehensive coverage – are not

always verified on the SHI market. Indeed, several empirical studies focusing on SHI markets,

either in the USA, in Australia or in the Netherlands, report ‘advantageous selection’ (Fang et al.

2008, Buchmueller et al. 2008, Bolhaar et al. 2008): healthier individuals are more likely to buy

insurance. This can be partly explained by institutional settings (employer-based contracts

for instance) or correlations between income, risk aversion and health. Especially, Hemenway

(1992) argues that advantageous selection can occur if highly risk-averse individuals are both

more likely to buy insurance and to make efforts to reduce their health risk. Advantageous

selection can also be the result of successful cream-skimming strategies from insurers who attract

individuals with lower risks. As a result, when insurance is voluntary, wealthier, younger and

healthier individuals are likely to get more comprehensive insurance coverage than the poor,

old and sick.

Because unequal insurance coverage eventually means unequal medical prices faced by patients,

the measure of a causal impact of SHI coverage on healthcare inequalities is incontestably of

interest. Yet, it is difficult to evaluate SHI impact empirically. Several papers identify significant

correlations between SHI coverage and healthcare consumption. In France, individuals with

SHI tend to visit specialists more often (Buchmueller & Couffinhal 2004). Van Doorslaer et al.


(2004) confirm that in France, Switzerland, Ireland and the UK, a significant part of pro-rich

inequity in healthcare use is linked to private health insurance. However, the positive correlation

between private insurance and healthcare use does not necessarily mean that SHI encourages

medical consumption. Indeed, selection effects are likely to explain a significant part of the

correlation. Nevertheless, Jones et al. (2006) use individual data from four different countries

(Italy, Portugal, Ireland and the UK) and show that even when controlling for selection bias,

SHI significantly increases visits to specialists. They also note that the rich are more likely to

buy supplemental coverage and therefore conclude that SHI contributes to ‘pro-rich’ inequalities

in the use of specialists. However, although it is crucial for policy recommendation, it remains

difficult to assess whether the increase in healthcare use due to SHI is a non-desirable over-

consumption or a desirable access effect.

Finally, the way SHI premiums are defined is responsible for most of the differences in ac-

cess, healthcare payments and possibly inequalities in healthcare use. Medical underwriting

or experience rating disadvantage sick individuals, age-based premiums make older age-group

contribute more, uniform premiums represent a higher share in poor households’ budgets and

income-based contributions might be difficult to impose to high-income groups. The impact of

SHI premiums on the distribution of healthcare payments is therefore also a critical question.

Objective of the thesis

This thesis deals with two questions relative to efficiency and fairness in mixed health insurance

systems with partial mandatory coverage and voluntary supplementary health insurance:

• the potential inflationary effect of supplementary insurance on medical prices;

• the fairness of supplementary insurance premiums in a context of voluntary insurance.

We set the analysis in the French context and perform empirical analyses on original individual-

level data, collected from the administrative claims of a French insurer (MGEN). The sample

is made of 99,878 individuals observed from 2010 to 2012.


The inflationary effect of SHI on medical prices: the case of balance billing coverage in France

The first two chapters focus on the inflationary effect of SHI on medical prices. In chapter I, we

estimate the causal effect of SHI on patient’s decision to consult physicians who balance bill their

patients, i.e. charge them more than the regulated fee set by NHI. Chapter II further investigates

the relationships between demand for balance billing, SHI coverage and moral hazard.

The relationship between balance billing and SHI coverage is symptomatic of the policy concerns

raised by voluntary SHI coverage, both on efficiency and equity grounds. On the one hand,

balance billing increases physician’s earnings with, in theory, no additional burden on the NHI.

It also allows patients to have access to a higher level of healthcare quality, by visiting highly-

skilled physicians and/or by reducing waiting time. They can also purchase SHI coverage to

limit OOP payments. On the other hand, because of moral hazard and unequal coverage, there

are rising concerns about an increase in medical prices and inequalities of access to specialists.

In France, for the last 15 years, the continuous increase in balance billing, that now amounts

to e2.3bn, has been concomitant with an extension of balance billing coverage by SHI. Still,

coverage remains very unequal and half of the population states that it is not well covered

against balance billing. This situation is not specific to France: Canada, Australia, Belgium,

the USA and the UK share the same concerns. There is indeed a crucial need for evidence on

the causal effect of SHI on the demand for balance billing as well as insights on potential access

problems.

Our investigation on the impact of SHI coverage on balance billing is also motivated by the

opportunity to measure moral hazard on two dimensions of healthcare use: quantity and quality.

When changes in prices are marginal, the impact on the number of visits to a specialist can be

rather low (Chiappori et al. 1998), either because of a low price-elasticity of healthcare demand

or because of important non-monetary costs due to waiting lists or travel time that reduce the

impact of insurance on the real price face by patients (Phelps & Newhouse 1974). However, the

impact is potentially much higher when SHI covers medical goods with a higher level quality.

Indeed, even if they do not visit specialists more often, individuals can use their SHI coverage to

visit more expensive physicians. This substitution effect eventually increases the average price

of healthcare.


Finally, voluntary SHI necessarily yields selection phenomena which are interesting from both

methodological and policy points of view. Indeed, contracts with more comprehensive coverage

may attract individuals whose healthcare consumption would increase more strongly. Defined

as ‘selection on moral hazard’ by Einav et al. (2013), this phenomenon has yet received little

attention in the literature. The French context with SHI coverage on balance billing is particu-

larly appropriate for investigating selection on moral hazard. Indeed, the demand for specialists

who balance bill relies strongly on preferences and beliefs in quality of care. These unobservable

characteristics may influence both the response to better coverage and the decision to take out

SHI, resulting in selection on moral hazard. As regards econometrics methods, taking into ac-

count selection on moral hazard requires to model explicitly the effect of individual unobserved

heterogeneity in the demand for healthcare, in the demand for coverage and in moral hazard.

From a policy point of view, considering the relationships between demand for higher quality

of care, demand for SHI coverage and the response to better coverage also gives insights on the

role of health insurance, especially in terms of access to care.

Are SHI premiums fair? The impact of age-based premiums on risk sharing and vertical equity

In the third chapter, we focus on the equity concerns raised by the generalization of age-based

premiums in the French SHI market. The French SHI market has two important features: in-

surance is voluntary and insurers can compete on premiums and coverage. Twenty years ago,

not-for-profit insurers, the mutuelles, provided most of the SHI contracts. These contracts usu-

ally took the shape of a unique plan: standardized coverage financed through uniform premiums,

i.e. a flat fee, independent from individuals’ characteristics. However, new entrants, attracted

by the increase in SHI perimeter, tend to provide tailor-made contracts with premiums adjusted

on the individual risk. The mutuelles are experiencing the ‘adverse selection death-spiral’ (Cut-

ler et al. 1997): they lose their low-risk clients attracted by lower premiums. The higher share

of high-risk in a mutuelle’s portfolio yields an increase in premiums and speeds up the loss of

low-risk. To survive, the mutuelles give up on uniform premiums and price their contracts with

premiums increasing with age in order to be closer to the individual risk. In 2005, only 66% of

SHI contracts provided by the mutuelles in the individual market were priced with age-based

premiums. It now concerns 90% of the contracts. By regulating the individual health insurance


market, the USA are experiencing an opposite change. The Affordable Care Act (ACA) bans

medical underwriting, a practice that strongly disadvantage sick people, and only allows insur-

ers to adjust premiums on age and gender. In this context, compared to medical underwriting,

age-based premiums are regarded as a movement toward more community rating.

Age-based premiums raise concerns about inequalities both in the level of premiums and in

the extent of coverage. Correlations between age, income and healthcare consumption make

it difficult to predict the impact of age-based premiums on transfers between low and high

healthcare users and high and low income groups. Furthermore, because age-based premiums

are a cross-breed between CR and actuarial fairness principles, they are likely to limit the

death spiral without preventing it completely: in each age-group, the lower risk might still have

incentives to remain uninsured or ask for lower premiums. The theoretical literature essentially

focuses on efficiency issues and barely analyzes the distributional impact of health insurance

premiums. On the other hand, empirical contributions focus essentially on vertical equity

and tend to ignore the adverse effects of a voluntary insurance. More importantly, because

the literature usually considers only the NHI level, results are difficult to generalize to the SHI

context. Indeed, SHI is meant to cover a different type of risk than NHI. Especially in the French

context where NHI covers inpatient care and does not charge co-pays for patients with chronic

disease, expenditures covered by SHI are likely to be less extreme, possibly more predictable for

the individuals too. For the same reasons, adverse selection phenomena, well documented in

the case of basic health insurance, might be different in the SHI market. Furthermore, because

of a lack of data, we have seldom knowledge about the distribution of healthcare expenditures

effectively covered by SHI. Correlations between SHI reimbursements, age, income and health

condition, which are critical to understand the distributional impact of age-based premiums,

have not been documented either.

To bridge this gap, we exploit an original database of 87,110 individuals, aged from 25 to 90

years-old, for whom we observe their SHI reimbursements and final OOP. We focus on ex post

outcomes to fully take into account the specificity of SHI in terms of distribution of expenditures

and correlations with age, income and health status. Our objective is to compare the impact

of age-based premiums with other regimes of premiums on the extent of transfers between low


and high users of healthcare (‘risk sharing’) and between low and high income groups (‘vertical

equity’).

Methodology

In this section we present our methods and the data we use. Our empirical strategy is meant to

deal with the challenges implied by a voluntary health insurance, especially selection phenom-

ena. Our estimates are based on an original dataset that provides, for the period 2010-2012

and across 99,878 individuals, detailed information on healthcare expenditures, NHI and SHI

reimbursements as well as OOP expenditures.

Methods

Identifying the causal impact of SHI on balance billing consumption

Estimating the causal impact of health insurance coverage on healthcare consumption represents

an empirical challenge. Indeed, when individuals can choose their level of coverage, the observed

relationship between insurance coverage and healthcare is influenced by endogeneous selection.

Unobserved individual characteristics are likely to explain both healthcare consumption and

the demand for better coverage. Different empirical strategies can be implemented to deal with

selection. One can consider exogeneous changes in the level of coverage, either by creating an

experimental design (Manning et al. 1987, Newhouse 1993) or exploiting quasi-natural experi-

ments (Chiappori et al. 1998). Studies that use cross section data often rely on simultaneous

equation methods to control for selection (Cameron et al. 1988, Holly et al. 1998). We use

individual panel data and estimate the causal effect of SHI on balance billing on individuals

who initially were not covered against balance billing and decided to enhance their coverage.

We control for selection by using individual fixed effects and instrumental variables. Individual

fixed effects control for unobserved characteristics likely to explain balance billing consumption.

Instrumental variables control for the non exogeneity of the decision to switch: our instruments

explain the decision to take out better coverage but are not correlated with a change in balance

billing consumption.


Taking into account the heterogeneous impact of SHI and possible selection on moral hazard

As mentioned previously, the decision to take out insurance may not only be related to heteroge-

neous demand for healthcare (‘classical adverse selection’) but also to heterogeneous response to

better coverage (‘selection on moral hazard’). In the econometric literature, selection on moral

hazard is more generally known as selection on returns or essential heterogeneity. Marginal

treatment effects (MTE) estimators have been developed to capture the impact of a treatment

likely to vary within a population in correlation with observed and unobserved characteristics,

in a setting where individuals select themselves into treatment. First defined by Bjorklund

& Moffitt (1987), MTE have been comprehensively described by Heckman & Vytlacil (2001)

and Heckman et al. (2006). We argue that MTE are appropriate tools to investigate the effect of

voluntary SHI on the demand for balance billing. First, MTE allow for heterogeneity in moral

hazard and can identify selection on moral hazard. Second, MTE rely on a structural approach

that links the output (the demand for balance billing), the decision to take the treatment (take

out SHI) and the treatment effect (moral hazard). We can therefore associate the heteroge-

neous treatment effect to different mechanisms related to income, supply side constraints or

preferences. In other words, we are able to give some ‘content’ to moral hazard, especially in

terms of access to specialists, and go beyond the homogeneous price effect usually reported in

the literature.

Simulating the impact of age-based premiums on risk sharing and vertical equity

Questioning the fairness of age-based premiums presents a double methodological challenge.

The first challenge lies in the measure of fairness. Besides the difficulty to define what a fair

premium is, we also need a synthetic measure in order to compare the respective impact of

different regimes of premiums. First, we choose to focus on ex post outcomes and precisely

what we call ‘healthcare payments’, i.e. premiums paid and OOP payments. Second, we focus

our analysis on the distribution of healthcare payments among low and high healthcare users

(‘risk sharing’) and low and high income groups (‘vertical equity’). We rely on the literature

on equity in healthcare finance (Wagstaff & Van Doorslaer 2000) and use inequality indexes

and concentration curves to compare the impact of different types of premiums. An original


contribution of our work is to adapt the indexes traditionally used for the measure of vertical

equity to also evaluate the impact of premiums on risk sharing.

Second, it is not possible to directly observe the impact of the way premiums are defined on

ex post outcomes. Because of the diversity of contracts available in the French SHI market,

the observed enrollment rates, average premiums paid and OOP payments will be the result

of various premiums regimes and coverage levels. Therefore, we use a simulation approach to

study how age-based premiums impact the distribution of healthcare payments. We define a

simplified framework where there is only one standardized SHI contract (one type of premium

and one level of coverage): individuals have only the choice to take out SHI or not. In this

framework, we are able to compute different types of premiums, predict whether individuals will

take out SHI or not and calculate their subsequent premium and OOP payments. We calibrate

the simulation with individual level data from MGEN for which we know that all policyholders

benefit from exactly the same level of coverage. Our simulations are not meant to have a strong

predictive power. However, they illustrate how SHI age-based premiums impact the distribution

of healthcare payments, given correlations between age, risk and income and adverse selection

phenomena.

Data

Our empirical investigations are performed on individual-level data collected from a French

insurer, the Mutuelle Générale de l’Education Nationale (MGEN). For historical reasons, MGEN

processes claims on behalf of NHI for teachers and ministry of education employees. MGEN also

provides voluntary SHI coverage (MGEN-SHI) which takes the shape of a unique contract: the

level of coverage is identical for all MGEN-SHI policyholders and premiums depend on income

and age.

Twelve months have been necessary to build a database relevant for research from raw expenses

claims. The sample has been randomly drawn from the 2.3 million individuals for whom MGEN

processes both NHI and SHI claims. We systematically checked for observations with errors and

missing data. The final sample is made of 99,878 individuals. From January 2010 to December

2012, we observe their annual consumption of healthcare as well as reimbursements from the


NHI and from MGEN-SHI. Our population is made of two different goups: (i) a representative

sample of MGEN enrollees for which MGEN processes NHI claims and who are covered by

MGEN-SHI from January 2010 to December 2012, we call them the ‘stayers’, and (ii) all the

individuals who were covered by MGEN-SHI in 2010 and switched to another insurer in 2011,

we call them the ‘switchers’. From January 2012, the switchers have therefore a different SHI

contract than the stayers. However, because MGEN still processes switchers’ NHI claims, we

are still able to observe their healthcare consumption.

As regards healthcare consumption, our database includes the number of acts, annual healthcare

expenditures as well as NHI and SHI reimbursements for different type of care: GP consulta-

tions, specialists consultations (including the specialty), technical acts, dental care, optical care,

the number of days spent in hospital4. We also have at our disposal socio-demographic infor-

mation on gender, age, place of residency and whether individuals are diagnosed with a chronic

disease. We use the fact that MGEN premiums depend on wages to reconstruct a proxy for

individuals income. This information is updated at the beginning of each year. We also add

data related to supply side organization, precisely the number of specialists for 100,000 inhab-

itants who do and do not balance bill at the département level. Data stem from the Syndicat

National Inter Régimes and are provided by the NHI (Caisse Nationale d’Assurance Maladie

des Travailleurs Salariés).

Building an individual-level database suitable for econometric analysis from raw administrative

data is long work which took almost a year. The different steps imply getting authorization

from the insurer, identifying relevant variables, designing the sample, writing endless SQL

codes, monitoring the extraction of variables and finally building individual-level panel data.

Nevertheless, it was worthwhile to devote to the building of this original database which is

an incredible source of information on the role of SHI in the consumption of healthcare. The

existing individual-level databases in France do not link NHI and SHI reimbursements. They

are also mostly cross-sectional or without many observable shock in terms of coverage which

preclude the identification of causal impacts. On the contrary, our MGEN database stems from

administrative data which provide reliable information on healthcare consumption as well as

4We were not able however to reconstruct healthcare expenditures during the hospital stay


NHI and SHI reimbursements. We are especially able to measure the final OOP, after NHI and

SHI reimbursements. Our two subsamples, the ‘stayers’ and the ‘switchers’ are used respectively

as a control and a treatment group and allow us to estimate a causal impact of SHI coverage

on healthcare consumption.

Outline

This thesis considers mixed health insurance systems where individuals can voluntarily purchase

SHI coverage in a market where neither the benefit package nor premiums are standardized.

Chapter I focuses on the inflationary effect of SHI on medical prices and estimate the causal effect

of SHI on patient’s decision to consult expensive physicians. Chapter II further investigates the

relationships between demand for healthcare, SHI coverage and moral hazard with a model

that allows heterogeneity in moral hazard. Chapter III analyzes the impact of SHI age-based

premiums on risk sharing and vertical equity when insurance is voluntary.

Chapter I

In the first chapter, we measure the causal impact of SHI coverage on patient’s decision to

consult physicians who balance bill, i.e. charge more than the regulated fee set by the NHI.

We use individual-level panel data to estimate the impact on patient behavior of a better

coverage of balance billing taking into account supply side drivers. Our database stems from

administrative data provided by the MGEN. For the period 2010-2012 we are able to observe

healthcare claims, NHI and SHI reimbursements for 43,111 individuals. In 2010, the whole

sample was covered by the same SHI contract, MGEN-SHI, which does not cover balance billing.

We observe the same individuals in 2012 after that 3,819 among them had decided to switch

to other supplementary insurers which do cover balance billing. So we have at our disposal

a treatment group, the ‘switchers’ who increased their balance billing coverage between 2010

and 2012, and a control group, the ‘stayers’ who remained MGEN-SHI enrollees during the

whole period, with no balance billing coverage. We deal with the endogeneity of the decision to

switch by introducing individual fixed effects into the specifications and by using instrumental

variables for the estimations.


On the whole sample, we find that individuals respond to better coverage by increasing their

proportion of consultations of specialists who balance bill by 9%, resulting in a 32% increase

in the amount of balance billing per consultation. However, the magnitude of moral hazard

strongly depends on the availability of physicians who charge the regulated fee. We find no

evidence of moral hazard in areas where physicians who charge the regulated fee are readily

accessible. On the contrary, when physicians who charge the regulated fee are scarce, a change

in coverage has a strong impact: individuals raise their proportion of consultations of specialists

who balance bill by 14%, resulting in a 47% rise in the amount of balance billing per consultation.

In these areas where the supply of regulated fee consultations is very constrained, balance billing

coverage also leads to an increase in quantity of specialist consultations.

To sum up, we find evidence of a moral hazard effect on quality of care: an increase in the pro-

portion of consultations of specialists who balance bill. In addition, we find for some individuals

a moral hazard effect on quantity of care: better coverage leads them to increase their number

of consultations of specialists, which suggests that balance billing limited their access to spe-

cialists. Another important result is the absence of impact of better coverage when physicians

who charge the regulated fee are widely available, enabling people to choose between physicians

who balance bill and physicians who do not. These results suggest that the most appropriate

policy to contain medical prices is not to limit insurance coverage but to monitor the supply of

care in order to guarantee patients a genuine choice of their physicians.

Chapter II

In the second chapter, we further investigate the relationships between the demand for health-

care, the decision to take out health insurance and the behavioral response to better coverage.

When insurance is voluntary, the estimated relationship between healthcare use and insurance

is influenced by endogeneous selection: individual characteristics are likely to explain both in-

dividuals’ consumption of healthcare and decision to buy insurance. Following Einav et al.

(2013) we distinguish two forms of selection: classical adverse selection and selection on moral

hazard. Classical adverse selection is linked to individual heterogeneity as regards the demand

for healthcare. Because they consume more healthcare than others some individuals may decide

to buy insurance to be covered against this financial risk. Selection on moral hazard is linked


to individual heterogeneity as regards their response to better coverage. Individuals may buy

insurance because they expect an increase in their consumption due to better coverage.

We set the analysis in the French context where individuals can voluntary take out SHI which

covers medical services with higher quality and quicker access than the benefit package covered

by mandatory national health insurance (NHI). We focus on the demand for specialists who

balance bill their patients, i.e. charge them more than the regulated fee set by NHI. The demand

for specialists who balance bill relies on preferences and beliefs in quality of care. Individuals

are likely to be heterogeneous in their preferences and beliefs, while these unobservable char-

acteristics both drive demand for care and decision to take out SHI, resulting in selection on

moral hazard. Heterogeneity in moral hazard might as well be influenced by observable charac-

teristics, especially income. We can expect that low income individuals benefit more from the

income effect associated with better coverage and increase their balance billing consumption

more strongly than rich individuals.

In the econometric literature, selection on moral hazard is generally known as ‘essential het-

erogeneity’. Marginal treatment effects (MTE) estimators have been developed to capture the

impact of a treatment likely to vary across individuals, when they select themselves into treat-

ment (Björklund and Moffitt 1987; Heckman, Urzua, and Vytlacil 2006).

We use MTE to estimate the causal effect of SHI coverage on balance billing consumption.

We take into account observed and unobserved individual heterogeneity in the demand for

consultations with balance billing and in response to better coverage (moral hazard). Our

empirical analysis is built on a model that links (i) the demand for balance billing, (ii) the

decision to take out more comprehensive SHI and (iii) the behavioral response to better coverage.

Thanks to this unified framework we are able to give insights on the determinants of the demand

for higher quality of care and the role of health insurance in terms of access, especially for low

income individuals.

Our database stems from MGEN administrative data. In 2012, we observe, for 58,519 indi-

viduals, healthcare claims and reimbursements by the NHI and SHI. We take advantage of

two groups of individuals: the MGEN-SHI enrollees and the better-SHI enrollees. In 2012,


the MGEN-SHI enrollees have no balance billing coverage. On the contrary, the better-SHI

enrollees, who quit MGEN-SHI in 2011 for another SHI, now benefit from better balance billing

coverage than MGEN-SHI enrollees.

We find evidence of individual heterogeneity in the response to better coverage and of selection

on moral hazard. Individuals with unobservable characteristics that make them more likely to

ask for comprehensive SHI are also those who exhibit stronger moral hazard, i.e. a larger increase

in balance billing per consultation. As concerns the influence of observable characteristics, we

also find that individuals’ income is a determinant of balance billing consumption and influences

the behavioural response to better coverage. Without coverage, the poor consume less balance

billing than the rich but increase their consumption more sharply once covered. They are also

more likely to take out better coverage.

In a context where SHI is voluntary, the inflationary impact of SHI coverage on balance billing

might be worsened by selection on moral hazard. Our policy conclusions as regards the role of

income are of different nature. The negative effect of income on the demand for balance billing

consultations coupled with its positive effect on moral hazard provides evidence that insurance

plays an important role in terms of access to care for low-income individuals.

Chapter III

In the third chapter we focus on the equity concerns raised by the generalization of age-based

premiums in the French SHI market. Indeed, the mutuelles, not-for-profit insurers, are keeping

away from their founding solidarity principles. To avoid the adverse selection death spiral, they

give up on uniform premiums and set premiums increasing with age. Age-based premiums raise

concerns about inequalities both in the level of premiums and in the extent of coverage.

Because the theoretical and empirical literature usually only considers the NHI level, it is

critical to take into account the specificity of SHI in terms of correlations between age, income

and healthcare expenditures to illustrate adverse selection phenomenon and the distributional

impact of SHI premiums. Furthermore, due to a lack of data, we have seldom knowledge


about the distribution of healthcare expenditures effectively covered by SHI and their impact

on income distribution.

In a context of voluntary SHI, we investigate how age-based premiums impact the extent of

risk sharing between low and high healthcare users and the extent of income redistribution

between low and high income groups. We adopt an empirical approach and use simulations to

compare age-based premiums with other regimes. We focus on ex post outcomes to fully take

into account the specificity of SHI in terms of distribution of expenditures and correlations with

age, income and health status.

We consider a simple framework where individuals have only the choice to subscribe to SHI or

not. There is only one contract available with the same level of coverage and the same regime

of premiums for all policyholders. We focus on expenditures meant to be covered by SHI,i.e.

the part of healthcare expenditures not covered by NHI. Firstly, we use simulations to compute

different regimes of premiums (uniform, age-based, income-based, income-based adjusted with

age, medical underwriting and experience rating), predict whether individuals will take-out SHI

or not and calculate their subsequent healthcare payments (premiums plus OOP payments). We

allow for possible adverse selection effects when premiums are based on a form of community

rating. Secondly, we use concentration curves and equity indexes to measure the impact of

different regimes of premiums on income distribution. An original contribution of our paper

is to adapt these tools to measure the impact of premiums on transfers between low and high

healthcare users.

To take into account the specificity of SHI, the simulation model is calibrated with data stemmed

from MGEN. We use individual-level observations on 87,110 individuals, aged from 25 to 90

years old, who are all covered by the same SHI contract (MGEN-SHI) from January 2010 to

December 2012. Additionally to information on socio-economic characteristics and health state,

we are able to observe their healthcare expenditures, NHI and SHI reimbursements and their

final OOP.

Based on our simulations, we derive three results on the impact of age-based premiums in the SHI

market: (i) in a context of voluntary SHI, age-based premiums is the best solution to preserve


risk sharing; (ii) however, they achieve risk sharing at the expense of vertical equity; (iii) the

absence of a mandate limits the impact of SHI on risk sharing and vertical equity, especially when

premiums are based on a form of community rating. We show that in a context of voluntary

SHI, age-based premiums limit the effect of adverse selection and still allow risk sharing. This

would support the generalization of age-based premiums at the expense of uniform premiums

in France and the change from actuarial premiums to adjusted community rating in the USA.

However, our simulations also point out that age-based premiums yield regressive payments

and raise legitimate concerns about the affordability of insurance and income inequalities due

to healthcare payments.

This thesis is organized as follows. The main features of the French SHI market are presented as

a prelude. Chapter 1 estimates the causal impact of SHI coverage on patient’s decision to consult

physicians who balance bill their patients. Chapter 2 further investigates the relationships

between demand for healthcare, SHI coverage and moral hazard. Chapter 3 analyzes the impact

of age-based SHI premiums on risk sharing and vertical equity. The final section concludes.

Résumé

Objectifs de la thèse

Cette thèse est consacrée à deux questions en lien avec l’efficacité et l’équité des systèmes mixtes

d’assurance maladie où la couverture publique obligatoire peut être complétée par une assurance

privée (complémentaire santé) :

• le potentiel effet inflationniste des complémentaires santé sur le prix des soins ;

• l’équité des primes des complémentaires dans un contexte d’assurance facultative.

Le chapitre 1 estime l’effet causal d’une couverture complémentaire généreuse sur la consomma-

tion de dépassements d’honoraires. Le modèle développé dans le chapitre 2 tient compte du fait

que l’impact d’une meilleure couverture sur les dépassements (aléa moral) varie d’un individu

à l’autre et que cette hétérogénéité peut être corrélée à la demande d’assurance. Le chapitre 3

simule l’impact de la tarification à l’âge sur les niveaux de primes et la décision de s’assurer en

prenant en compte les corrélations entre âge, état de santé et revenu.

Méthode

Les analyses empiriques sont réalisées sur données françaises. Cette base de données originale

regroupe les consommations de soins de 99878 affiliés à la Mutuelle Générale de l’Education

Nationale (MGEN) entre 2010 et 2012.

La MGEN gère les remboursements pour le compte de l’Assurance maladie obligatoire, notam-

ment pour les employés du Ministère de l’Education Nationale. La MGEN propose également

30 Résumé

une couverture complémentaire facultative sous la forme d’un contrat unique : le niveau de cou-

verture est identique pour tous les affiliés et les primes dépendent majoritairement des revenus

salariés ou pensions de retraite des affiliés.

Près de douze mois ont été nécessaires pour construire cette base à partir des données admin-

istratives de la MGEN. Sur les 2,3 millions d’affiliés pour lesquels la MGEN gère à la fois la

couverture obligatoire et complémentaire, un échantillon de 99878 individus a été tiré aléatoire-

ment et anonymisé. De janvier 2010 à décembre 2012, nous observons leur consommation de

soins ainsi que les remboursements de l’assurance maladie obligatoire et complémentaire. Notre

échantillon est composé de deux groupes distincts : (i) un échantillon représentatif des affiliés

MGEN pour lesquels la MGEN gère à la fois la couverture obligatoire et complémentaire de

janvier 2010 à décembre de 2012, nous les appelons les « stayers » ; et (ii) l’ensemble des affiliés

couverts par la couverture complémentaire de la MGEN en 2010 mais qui ont décidé de souscrire

un nouveau contrat auprès d’un autre assureur en 2011, nous les appelons les « switchers ».

A partir de janvier 2012, les switchers ont par conséquent un contrat complémentaire différent

de celui des stayers. Toutefois, parce que la MGEN gère toujours leurs remboursements liés à

l’assurance maladie obligatoire, nous sommes toujours en mesure d’observer la consommation

de soins des switchers.

Pour ce qui est des consommations de soins, nous disposons pour chaque individu du nombre

de consultations, du total annuel des dépenses et des remboursements de l’assurance obliga-

toire et complémentaire pour différents types de soins : consultations généralistes et spécial-

istes (par spécialité), actes techniques, soins dentaires, optique ainsi que le nombre de jours

d’hospitalisation. Nous disposons également d’information socio-démographiques telles que le

genre, l’âge, le lieu de résidence ainsi que le statut ALD (affection longue durée). Nous util-

isons le fait que la MGEN calcule ses primes sur les revenus de ses affiliés pour reconstruire

un proxy du revenu individuel. Ces informations sont mises à jour au début de chaque année

civile. Des données sur la densité des médecins spécialistes dans le département de résidence

des affiliés (nombre de médecins spécialistes pour 100,000 habitants) viennent compléter la base

de données.

Le temps nécessaire à la construction d’une base de données adaptée à l’analyse micro économétrique

Résumé 31

à partir de données brutes administratives a été compensé par l’incroyable source d’information

que cette base offre quant au rôle de l’assurance complémentaire sur la consommation de soins.

Les bases existantes en France et en Europe ne font pas le lien au niveau individuel entre

remboursements de l’assurance obligatoire et des couvertures complémentaires facultatives. De

plus, les données disponibles sont généralement en coupe ou ne sont pas construites pour estimer

l’impact causal d’un choc de couverture. A l’inverse, notre base de données est issue de données

administratives qui permettent une analyse fiable et précise des consommations de soins et des

remboursements de l’assurance obligatoire et complémentaire. Nous sommes particulièrement

en mesure d’estimer le reste à charge final, après remboursements des assurances obligatoire et

complémentaire. Les deux groupes qui constituent l’échantillon, les « stayers » et les « switchers

», peuvent être utilisés respectivement comme groupe de contrôle et de traitement pour estimer

l’impact causal de la complémentaire santé sur la consommation de soins.

Résumé des chapitres

Chapitre 1

Le premier chapitre estime l’effet causal d’une couverture complémentaire généreuse sur la

demande de consultations de spécialistes qui pratiquent des dépassements d’honoraires, i.e.

pratiquent des tarifs supérieurs à ceux fixés par l’assurance maladie obligatoire.

Les données individuelles en panel issues de la MGEN sont utilisées pour estimer l’impact d’une

meilleure couverture des dépassements sur la demande de consultations des patients tout en

prenant en compte les effets d’offre. Sur la période 2010-2012 nous observons les demandes de

remboursements, adressées aux assurances obligatoire et complémentaire, de 43111 individus.

En 2010, la totalité de l’échantillon avait souscrit à la même complémentaire santé, la MGEN, qui

ne couvre pas les dépassements d’honoraires. Nous observons les mêmes individus en 2012 après

que 3819 d’entre eux aient décidé de changer leur couverture complémentaire. Comparé à leur

ancienne couverture, ce nouveau contrat ne peut être qu’identique ou plus généreux en termes de

couverture des dépassements. Nous disposons donc d’un groupe de traitement, les « switchers »

qui ont vu leur couverture contre les dépassements augmenter entre 2010 et 2012 et un groupe de

contrôle, les « stayers » qui sont restés affiliés à la couverture complémentaire de la MGEN (sans

32 Résumé

couverture des dépassements) de 2010 à 2012. La méthode des variables instrumentales associée

à la spécification d’effets fixes individuels dans les régressions en panel permet de contrôler de

la possible endogénéité liée à la décision de changer de contrat d’assurance.

Les résultats sur l’ensemble de l’échantillon montre que les individus qui bénéficient d’une

meilleure couverture complémentaire augmentent leur proportion de consultations avec dépasse-

ments d’honoraires (secteur 2) de 9% avec pour conséquence une augmentation de 32% du

montant moyen de dépassements par consultation. Toutefois, l’importance de l’impact dépend

fortement de la densité de spécialistes qui ne pratiquent pas de dépassements (secteur 1). Les

estimations ne montrent pas d’aléa moral dans les départements où l’accès aux spécialistes de

secteur 1 est facilité compte-tenu de leur forte densité sur le territoire. A l’inverse, quand la

densité de spécialistes de secteur 1 est faible, une modification de la couverture à un fort impact

sur la demande de dépassements. Les patients augmentent de 14% la proportion de consulta-

tions en secteur 2, entraînant une augmentation de 47% du montant moyen de dépassements

par consultation. Dans les départements où l’offre de consultations sans dépassements est très

restreinte, bénéficier d’une couverture contre les dépassements conduit également les patients à

augmenter leur nombre de visites spécialiste.

Les estimations montrent ainsi la présence d’aléa moral sur la qualité des soins via une aug-

mentation de la proportion de consultations avec dépassements d’honoraires. En outre, pour

certains patients l’assurance a un impact sur la quantité de soins : une meilleure couverture

des dépassements leur permet d’augmenter le nombre de visites chez le spécialiste. Ce dernier

résultat suggère que les dépassements d’honoraires pourraient créer des problèmes d’accès aux

soins. Un autre résultat important est l’absence d’effet d’une meilleure couverture dans les dé-

partements où les spécialistes de secteur 1 sont largement accessibles, ce qui permet aux patients

de choisir librement entre consultations avec ou sans dépassements.

En termes de recommandation de politique publique, ces résultats suggèrent que restreindre

l’accès à une couverture des dépassements d’honoraires ne semble pas être la mesure la plus

appropriée pour limiter l’effet inflationniste des couvertures complémentaires. Une régulation

de l’offre, pour assurer un libre choix entre spécialistes du secteur 1 et du secteur 2, respecterait

les préférences des patients pour les dépassements sans créer d’effet inflationniste.

Résumé 33

Chapitre 2

Le chapitre 2 analyse les relations entre la demande de soins, la décision de souscrire à une

assurance complémentaire et le comportement des individus une fois qu’ils sont mieux couverts.

Lorsque l’assurance est facultative, l’estimation de l’impact de l’assurance sur la consommation

de soins est influencée par des phénomènes de sélection : les caractéristiques individuelles peu-

vent expliquer à la fois la consommation de soins des individus et leur décision de souscrire à une

assurance. En se basant sur les travaux d’Einav et al (2013), nous distinguons deux formes de

sélection : l’antisélection classique (« classical adverse selection ») et la sélection sur aléa moral

(« selection on moral hazard). L’antisélection classique est liée à l’hétérogénéité individuelle

en termes de demande de soins. Certains individus peuvent consommer plus de soins que les

autres et décider de se couvrir contre ce risque financier. La sélection sur aléa moral réfère

à l’hétérogénéité individuelle en termes de réponse à une meilleure couverture. Les individus

peuvent vouloir se couvrir parce qu’ils anticipent que leur nouvelle couverture leur permettra

d’augmenter leur consommation de soins.

L’analyse empirique est menée dans le contexte français où les individus ont le choix de souscrire

une assurance complémentaire qui peut leur donner accès à des soins de meilleure qualité et à

des temps d’attente réduits comparé au panier de soins couvert par l’assurance maladie obli-

gatoire. L’analyse se focalise sur les dépassements d’honoraires. Les individus peuvent avoir

des préférences et croyances hétérogènes concernant la qualité associée aux consultations avec

dépassements. Ces préférences, inobservables pour l’économètre, sont susceptibles d’expliquer

à la fois la demande pour des consultations de secteur 2 et la demande pour une meilleure

couverture des dépassements, créant de la sélection sur aléa moral. L’hétérogénéité en termes

d’aléa moral peut également être expliquée par des caractéristiques observables telles que le

revenu. Les individus avec un faible revenu peuvent en effet bénéficier davantage que les autres

d’une couverture assurantielle en augmentant de façon plus importante leur consommation de

soins.

Dans la littérature économétrique, la sélection sur aléa moral renvoie au concept d’ « essential

heterogeneity ». L’estimateur des « marginal treatment effects » (MTE) a été développé pré-

cisément pour capturer l’impact d’un traitement susceptible de varier d’un individu à l’autre,

34 Résumé

lorsque ces individus ont le choix de participer ou non au traitement (Björklund and Moffit,

1987 ; Heckman, Urzua and Vytlacil, 2006).

Les estimations sont réalisées sur un échantillon de 58519 individus issus de la base de données

MGEN. Nous observons la consommation de soins et remboursements en 2012 de deux groupes

: les affiliés MGEN, qui ne sont pas couverts contre les dépassements et les individus qui

bénéficient d’une meilleure couverture complémentaire.

Les résultats montrent l’existence d’hétérogénéité individuelle dans la réponse à une meilleure

couverture et la présence de sélection sur aléa moral. Les individus dont les caractéristiques

inobservables les rendent plus à même de souscrire à une couverture complémentaire généreuse

sont aussi ceux qui augmentent le plus fortement leur consommation de dépassements une fois

couverts. En ce qui concerne les caractéristiques observables, le revenu apparait comme un

déterminant à la fois de la demande de consultations avec dépassements et de la réponse à

une meilleure couverture. Sans couverture contre les dépassements, les bas-revenu consomment

moins de dépassements que les haut-revenu mais augmente plus fortement leur consommation

une fois couverts. Ils sont aussi plus susceptibles de souscrire à une couverture complémentaire

plus généreuse.

Dans un contexte où la complémentaire santé est facultative, l’effet inflationniste de la couver-

ture contre les dépassements est accentué par un phénomène de sélection sur aléa moral. Les

conclusions tirées de l’impact du revenu sont d’une autre nature. L’effet négatif du revenu sur

la consommation de consultations avec dépassements associé à son effet positif sur la réponse à

une meilleure couverture témoignent du rôle critique de l’assurance concernant l’accès aux soins

des individus à bas-revenu.

Chapitre 3

Le troisième chapitre examine les questions d’équité soulevées par la généralisation de la tarifi-

cation à l’âge sur le marché français des complémentaires santé. Sous l’effet de la concurrence,

les mutuelles, assureurs sans but lucratif, s’éloignent de leurs principes fondateurs. Pour éviter

les phénomènes d’antisélection et de «spirale de la mort », les mutuelles abandonnent les primes

Résumé 35

uniformes au profit de primes augmentant avec l’âge, potentiellement au prix d’importantes

inégalités en termes de primes et de couverture.

La littérature théorique et empirique qui s’est intéressée à la tarification assurantielle ne consid-

ère généralement que le cas de l’assurance de base. Il est donc critique d’aborder ces questions

en prenant en compte les spécificités de l’assurance complémentaire et particulièrement les cor-

rélations entre âge, revenu et dépenses de santé pour illustrer les phénomènes d’antisélection

et mesurer l’impact redistributif des primes d’assurance complémentaire. Dans un contexte où

l’assurance complémentaire est facultative, nous simulons l’impact de la tarification à l’âge sur

la redistribution horizontale, entre malades et bien portants, et sur la redistribution verticale,

entre haut et bas revenus. L’impact de la tarification à l’âge est mesuré ex post et comparé à

d’autres formes de tarification.

L’analyse s’inscrit d’un cadre théorique simplifié, dans lequel les individus ont seulement le

choix de souscrire ou non un contrat d’assurance complémentaire. Il n’y a qu’un contrat pro-

posé avec le même niveau de couverture et le même régime de primes pour tous les assurés.

L’analyse empirique concerne uniquement la part des dépenses de santé qui peut être couverte

par l’assurance complémentaire, i.e. sur les dépenses qui ne sont pas couvertes par l’assurance

maladie obligatoire. La première étape consiste à simuler différents régimes de primes (primes

uniformes, tarification à l’âge, au revenu, primes basées sur l’âge et le revenu, « medical under-

writing » et « experience ration), prédire la demande individuelle pour le contrat d’assurance

complémentaire et calculer pour chaque individu les primes et reste à charge en fonction de leur

décision d’être couverts ou non. Lorsque le régime de primes repose sur une forme de « com-

munity rating », les effets d’antisélection sont pris en compte dans la simulation. La deuxième

étape mesure l’impact des différents régimes de primes sur la distribution de revenu ex post à

partir de courbes de concentration et d’index d’inégalités. Une contribution méthodologique

importante de ce chapitre est d’adapter ces outils à la mesure des transferts entre malades et

bien portants.

Le modèle est calibré sur les données de la MGEN. Nous utilisons les données de 87110 individus,

âgés de 25 à 90 ans, qui sont tous couverts par le même contrat d’assurance complémentaire de

janvier 2010 à décembre 2012. Nous observons leur revenu, leurs dépenses de soins annuelles,

36 Résumé

les remboursements de l’assurance obligatoire et complémentaire ainsi que leur reste à charge

final.

Les simulations donnent trois résultats principaux : (i) dans un contexte d’assurance facultative,

la tarification à l’âge est le régime le plus à même de préserver la redistribution horizontale ; (ii)

en revanche, cela se fait au détriment de la redistribution verticale ; (iii) l’absence d’une obliga-

tion de s’assurer limite l’impact de l’assurance complémentaire sur la redistribution horizontale

et verticale, notamment lorsque le régime de primes est basé sur une forme de « community

rating ».

Lorsque l’assurance est facultative, la tarification à l’âge limite donc l’antisélection et permet

d’assurer une forme de redistribution horizontale. Ce résultat tend à supporter le mouvement

des mutuelles vers la tarification à l’âge. En revanche, les simulations montrent également que

la tarification à l’âge induit des paiements régressifs et crée des inquiétudes légitimes quant à

l’accessibilité financière de l’assurance complémentaire et aux inégalités de revenus accentuées

par les dépenses de santé.

Prelude

The French supplementary health insurance market

The French health insurance system is a mixed system based on a mandatory, universal yet par-

tial National Health Insurance (NHI). The NHI is mainly funded through contributions based

on income and organized by a single payer. The private health insurance market provides con-

tracts that have both complementary and supplementary features. For the sake of simplicity, we

will refer to the French private health insurance market as a ‘Supplementary Health Insurance’

market (SHI). SHI contracts usually cover at least co-payments but most of them also cover

medical goods and services out of the public benefit package such as complex dental care, opti-

cal devices, alternative medicines as well as private practice in hospitals or visits to physicians

out of the regulated fee system. The way premiums are defined varies from pure CR to medical

underwriting, even income-based premiums for some employer-based contracts and few not-for

profit insurers. Age-based premiums are widespread though on the individual market.

Although voluntary, SHI coverage is considered as essential in access to care in France. Indeed,

OOP expenditures are not capped and can represent an important part of individuals’ budget.

Public programs therefore provide either free SHI or vouchers to low-income groups5 ensuring

that vulnerable individuals will be at least covered for co-payments. Patients with chronic

disease6 are also exonerated from co-payments for healthcare related to their condition. Since

2016, all private sector employers, even small businesses, also have to provide subsidized health

insurance coverage to their employees. However SHI is still voluntary in the individual market.

5These programs are known as Couverture Maladie Universelle Complémentaire (CMU-C) and Aide aupaiement d’une Complémentaire Santé (ACS)

6Affection Longue Durée (ALD)

38 Prelude

One of the reason could be that supplementary insurance covers luxury medical goods, that do

not raise any equity concerns. There are two limits to this reasoning. First, the frontier between

complementary and supplementary coverage is actually not always easy to draw, especially for

visits to physicians. Indeed, in France, some physicians, mostly specialists, are allow to balance

bill their patients, that is charge them more than the regulated fee. As a result, on top of

co-payments, patients bear more or less out-of-pocket expenses depending on their coverage.

A limited SHI coverage can therefore limit access to specialists, as co-payments would do.

Second, by separating basic from supplementary healthcare and coverage issues, we tend to

ignore spillover effects, which can be important especially on medical care prices.

In 2014, 13.5% of the total healthcare expenditures have been financed through the SHI market

in France. Indeed, the NHI is universal yet partial and covers on average 78% of the total

healthcare expenditures. The remaining 8.5% is directly borne by households. Although health

insurance systems combining public and private funds are common among OECD countries, the

French health insurance system remains very peculiar. First, the share of expenditures funded

through SHI is one of the most important among European countries (Figure 1). Second, the

market is very competitive and far less regulated in terms of benefit package and premiums

than the German, Dutch or Swiss systems.

The increasing role of SHI in France

It might be puzzling to notice that the relatively high rate of public coverage in France did not

prevent the SHI market from expanding. The reasons are historical, economical and political.

Back in 1900, private health insurers, essentially not-for-profit companies, were already pro-

viding health insurance coverage to almost 2 million individuals. When the mandatory public

scheme, the Sécurité sociale, has been endorsed in 1946, private insurers bridged the gap left by

a partial public coverage (about 60% of total expenditures) by offering complementary health

insurance. They have seen their market share increased since, especially from the end of the 80’s,

taking advantage of the combined effects of a continuous increase in healthcare expenditures

and the political will to slow down public expenditures. To be fair, the average share of public

funding did not dramatically drop: it reached its maximum in 1980 with a 80% coverage, and

has decreased since to amount 76%. However, this statement hides two important facts. First,

Prelude 39

in absolute terms, the constant increase of health expenditures logically increases year after

year the potential size of the SHI market: from 33.5 billion euros in 2006 to 41.9 billion euros in

2014. Average figures can also be misleading. First, the average NHI coverage drops to 64% for

ambulatory care and 32.5% for dental care (Figure 2). Second, public expenditures are highly

concentrated on patients with chronic diseases who benefit from complete coverage for health-

care related to their condition. As a result, the average NHI coverage for individuals without

co-payment exemption (that is 87% of the population) only reaches 55%. Finally, considering

the highly skewed distribution of healthcare expenditures and the absence of any mechanism to

cap OOP payments, the financial risk borne by households after NHI reimbursements remains

important. Focusing on the top of the distribution of expenses after public reimbursements,

5% of the population has OOP payments that exceed e1600 per year (HCAAM, 2009). OOP

expenses rise above e3250 for the last centile.

Although 95% of the French population declares to be covered by a SHI contract, inequalities

are striking. Indeed, this high coverage rate hides an important heterogeneity in terms of

coverage and premium paid. One of the consequences is that access to SHI strongly depends

on occupation and income (Figures 3 and 4). Very low-income individuals, who represent

6% of the population, benefit from a public supplementary coverage (CMU-C). Individuals

who work in the private sector and their families benefit from employer-based contracts, largely

subsidized and usually financed through community rating. These contracts also offer on average

more generous coverage. In 2014, 35% of the population was covered with an employer-based

contract (DREES 2016). The remaining 54%, mostly students, independent and part-time

workers, civil servants and pensioners have access to supplementary coverage only through

the individual market where premiums mostly depend on age. The extent of coverage varies

also dramatically from a contract to another which is likely to create unequal access to care,

especially when it concerns co-payments on basic healthcare. For instance, 80% of individuals

insured with an employer-based contract are covered for balance billing, and therefore benefit

from an easy access to specialists. They are only 40% in the individual market.

40 Prelude

A competitive and attractive market

Not-for-profit and for-profit companies compete in the SHI market, offering individual as well as

employer-based coverage. The historical mutuelles, not-for-profit organizations, still outnumber

commercial insurance companies but the market keeps on being more and more concentrated

(Figure 5). Insurance companies are seeking for critical size to deal with a highly competitive

market as well as more and more demanding prudential rules. This is especially true for not-

for-profit insurers for whom health insurance is their main activity and represents 84% of their

revenues on average. On the contrary for-profit companies consider health insurance more

as a diversification strategy (only 5% of their revenues) and are likely to benefit from higher

scale returns and network externalities. In 2002, there were 1,520 distinct companies in the SHI

market, but 120 only were for-profit. In 2014, the market counted only 573 businesses, including

94 for-profit (DREES 2016). The top 10 of health insurers, each with a revenue over 1 billion

euros, account for 35% of market-wide revenues. Although the SHI market is highly subsidized

through tax exoneration for employer-based contracts and vouchers for low-income individuals,

it is also heavily taxed. Not-for-profit insurers used to benefit from a lower tax rate, around

3.5%. Since 2012 however, their tax rate has been increased to reach 7% of their revenues, a

similar rate than for for-profit companies.

Segmented contracts and age-based premiums

Not-for-profit insurance companies are progressively loosing market shares on both individual

and employer-based contracts; it dropped from 60% in 2001 to 53% in 2014 (Figure 6). In this

respect, the situation is quite similar to what Blue Cross and Blue Shield experienced on the

American market (Thomasson 2002). These not-for-profit insurers also used to rely on solidar-

ity principles with community rating and generous coverage. However, they could not compete

with actuarial premiums and tailor-made contracts offered by for-profit companies which espe-

cially attract young and healthy individuals. Most of the not-for-profit companies disappeared

and those who survived had to abandon uniform premiums and offer contracts with higher

deductibles. Though limited by higher public coverage rates than in the USA (Buchmueller

& Couffinhal 2004), we can observe the same adverse selection effects on the French market,

especially for individual coverage. While uniform premiums and equal coverage were the two

Prelude 41

founding principles of the mutuelles, more than 90% of the contracts are now priced with age-

based premiums and the market has never been so segmented. Note that experience rating is

forbidden in France7 and insurers have strong fiscal incentives to avoid medical underwriting8.

Therefore, age remains the only predictor for the individual risk. Fiscal incentives also con-

strain insurers to offer a minimal coverage, i.e. reimbursements of NHI co-pays for ambulatory

and inpatient care. Yet, insurers target low risks by tailoring contracts with different levels of

coverage for medical goods outside of the NHI benefit package: birth control, optical and dental

care, hearing devices or balance billing.

As a result, the unregulated competition on the SHI market, where companies offer dozens

of contracts with heterogeneous coverage and premium schemes, not only prevent consumers

from comparing offers but also rise serious concerns about the efficacy and fairness of the

French health insurance system. A French survey conducted in 2013 (DREES 2016) reveals

indeed important differences in the extent of coverage among age groups (Table 1). Especially,

individuals over 60, despite increasing medical needs, appears to be less covered on all types of

care than individuals between 25 and 59 years old.

7Loi n° 89-1009 du 31 décembre 1989, Loi Évin8To be certified by the French government as ‘Contrats solidaires’, insurers cannot use medical questionnaires

42 Prelude

Tables and Figures

Figure 1 – Financing health care: international comparison

Figure 2 – Average coverage by type of care in France in 2014

Prelude 43

Figure 3 – SHI coverage in France in 2014: type of contracts by occupation

Figure 4 – SHI coverage in France in 2014: type of contracts by income groups

44 Prelude

Figure 5 – Number of firms on the French health insurance market, 2001-2014

Figure 6 – Market shares on the French health insurance market, 2001-2014

Prelude 45

Table 1 – Average coverage in euros, by age-group, in 2013

Type of medical care under 25 y.o 25-59 y.o 60+ y.o

Visit to a specialist 12 18 13Surgeon fees 117 192 135Simple optical devices 155 230 181Complex optical devices 237 361 282Hearing devices 585 1,012 928DREES, 2016

Chapter 1

Does health insurance encourage the

rise in medical prices? A test on

balance billing in France

1.1 Introduction

Designed to favour access to care for all, social health insurance is widespread in the European

Union and most developed countries. Many debates have focused on the ability of health care

systems to contain health expenditure growth, but little attention has been devoted to the fact

that effectiveness of coverage depends on the regulator’s ability to control medical prices. For

ambulatory care, national health insurance (NHI) systems usually set prices or sign agreements

with physicians that set a regulated fee, which is the basis for NHI reimbursement. Nevertheless,

physicians can sometimes balance bill their patients, i.e. charge them more than the regulated

fee.1 Because balance billing can generate high out-of-pocket expenditures, patients often pur-

chase supplementary health insurance (SHI) to cover this financial risk. However, generous

health insurance coverage can cause welfare loss, not only because it might favour excessive

consumption of care, but also because healthcare providers can increase their prices (Pauly

1968, Feldstein 1970, Feldman & Dowd 1991). Hence, comprehensive coverage might encourage

This chapter was jointly written with Brigitte Dormont. It has been published in Health Economics.1The terms "extra billing" or "dépassements d’honoraires" (in French) can also be found in the literature

48 Chapter1

demand for expensive physicians, resulting in an increase in balance billing. This increase leads

to a rise in SHI premiums, and jeopardizes coverage for patients who are covered by NHI alone.

The aim of this paper is to measure the causal impact of a positive shock on SHI coverage on

recourse to physicians who balance bill. The econometric analysis is performed on a French

database of 43,111 individuals observed between 2010 and 2012 and covers specialist consulta-

tions in ambulatory care. In addition to measuring the impact of insurance coverage on balance

billing, we address two related issues: the influence of supply organization on balance billing

(i.e., ease of access to physicians who do not balance bill) and the possible impact of balance

billing on access to care.

Balance billing became a political issue in the USA in the late 1980s. Physicians were allowed to

charge Medicare patients more than the copayment set by Medicare, the social health insurance

system for people aged 65 or more. In 1984, balance billing amounted to 27% of total out-

of-pocket payments charged to Medicare beneficiaries for physician consultations. Concerns

about possible degradation of healthcare coverage led several states to restrict balance billing,

and the federal government followed suit. The Omnibus Budget Reconciliation Act of 1989

restricted balance billing. It was eventually limited to a maximum of 9.25% of the Medicare

fee in 1993 (see McKnight (2007) for a full description of Medicare’s balance billing reform).

Balance billing for physician visits and hospital stays also exists in Canada, Australia, France

and Belgium (Epp et al. 2000, Gravelle et al. 2013, Lecluyse et al. 2009).

In France, a large proportion of specialists are allowed to balance bill their patients. The

population is covered by mandatory NHI and for each service provided, a reference fee is set by

agreement between physicians and the health insurance administration. NHI covers 70% of the

reference fee for ambulatory care. Individuals can take out supplementary private insurance:

either voluntarily on an individual basis, or through occupational group contracts. Currently,

95% of the French population is covered by SHI. Supplementary insurance contracts cover the

30% of ambulatory care expenses not covered by NHI. In addition, they can offer coverage for

balance billing.

Concern about balance billing is mounting in France because it has doubled over the last 15

1.1 Introduction 49

years and now represents 2.3 billions euros. This expansion is due to an increase in both the

average amount of balance billing – which rose by an average 1.7% per year between 2004

and 2011 (DREES 2013)– and the share of doctors (mostly specialists) who balance bill their

patients. For policy makers, balance billing has the advantage of permitting an increase in

physicians’ earnings with no additional burden on social health insurance. However, it raises

out-of-pocket payments and might lead to a two-tier healthcare system where only rich people

can afford to see certain doctors. Moreover, the last 10 years have been marked by continuous

extension of balance billing coverage by supplementary insurers, together with a continuous

increase in the amount of balance billing. This suggests that coverage encourages balance

billing. In keeping with this idea, the French government has recently introduced tax reductions

for insurers who offer contracts that limit coverage of balance billing.

Balance billing in the context of social health insurance raises several policy questions. Should

it be forbidden? Should it be restricted, as for Medicare patients in the USA? Should coverage

of balance billing be discouraged as in France? On the contrary, should the government favor

balance billing to promote better care quality? Or should the government only monitor the

supply of care, to ensure that all patients have a genuine choice, i.e. effective access to physicians

who do not balance bill?

In this paper, we evaluate the impact on patient behavior of a shock consisting of better coverage

of balance billing, while controlling for supply side drivers. In our framework, the impact of

coverage on healthcare use depends both on patients’ beliefs regarding the quality of care

provided by physicians who balance bill, and on access to physicians who do not balance bill.

Focusing on balance billing enables us to study the impact of insurance coverage (moral hazard)

on two dimensions of care use: quality and quantity.

Our database stems from administrative data provided by the Mutuelle Générale de l’Education

Nationale (MGEN). We use a panel dataset of 43,111 individuals observed between January 2010

and December 2012, which provides individual information on healthcare claims and reimburse-

ments provided by national and supplementary health insurance. Our data make it possible to

observe enrollees when they are all covered by the same supplementary insurer (MGEN-SHI),

which does not cover balance billing, and after some of them switched to other supplementary

50 Chapter1

insurers which do cover balance billing. So, we have at our disposal a treatment group, the

’switchers’, and a control group, the ’stayers’, made up of those who did not leave MGEN sup-

plementary insurance. Because the decision to switch to a more generous insurance coverage is

likely to be non-exogenous, we introduce individual fixed effects into the specifications and use

instrumental variables for the estimations.

On the whole sample, we find that better coverage leads individuals to raise their proportion of

consultations of specialists who balance bill by 9%, resulting in a 32% increase in the amount

of balance billing per consultation. However, the impact of the coverage shock depends on

local availability of physicians who charge the regulated fee, measured by the local specialist :

population ratio for these physicians. We find that a coverage shock has no significant effect

on recourse to expensive physicians or on the amount of balance billing when physicians who

charge the regulated fee are readily accessible. On the contrary, when physicians who charge the

regulated fee are scarce, a coverage shock has a strong impact: individuals raise their proportion

of consultations of specialists who balance bill by 14%, resulting in a 47% rise in the amount of

balance billing per consultation; in addition, there is evidence of limits in access to care for a

sizeable minority of individuals in this situation (30% of the sample).

To sum up, we find evidence of a moral hazard effect on quality of care: an increase in the

proportion of consultations of specialists who balance bill. In addition, we find for some indi-

viduals a moral hazard effect on quantity of care: better coverage leads them to increase their

number of consultations of specialists, which suggests that balance billing limited their access

to specialists. Another important result is the absence of impact of a coverage shock when

physicians who charge the regulated fee are widely available, enabling people to choose between

physicians who balance bill and physicians who do not. On the basis of these results, it seems

that the most appropriate policy is not to limit insurance coverage but to monitor the supply

of care in order to guarantee patients a genuine choice of their physicians.

This paper is organized as follows. Section 1.2 summarizes the related literature. Section 1.3

describes French regulation of ambulatory care, and formalizes patients’ decisions to consult a

physician who balance bill in the French context. In section 1.4, we present our data and em-

1.2 Insurance coverage, medical prices and balance billing: results from the literature 51

pirical strategy. Econometric specification and estimation are presented in section 1.5. Results

and robustness checks are presented in section 1.6 and section 1.7 concludes.

1.2 Insurance coverage, medical prices and balance billing: re-

sults from the literature

The literature devoted to the impact of health insurance on the market for health care can shed

light on the question of the impact of health insurance on balance billing. If more insurance raises

demand, this should increase medical prices. Papers studying the influence of health insurance

on suppliers’ medical pricing date from the 1970s. According to Feldstein (1970, 1973) physicians

respond to health insurance coverage by increasing their fees. Using US data, Sloan (1982)

showed that a $1 increase in health insurance coverage results in a 13 to 35 cents increase in

physicians’ fees. These results are in line with theoretical predictions (Chiu 1997, Vaithianathan

2006). On the demand side, moral hazard depends on the sensitivity of demand to prices (Einav

et al. 2013): assuming a negative price-elasticity of demand, better coverage leads to an increase

in health care use. However, as pointed out by Phelps & Newhouse (1974), the impact of

insurance coverage on demand for health care may depend significantly on time costs associated

to access to a doctor, such as travel time or queues in the office. Demand for goods with relatively

low time costs is likely to be more sensitive to a change in health insurance coverage.

What is the impact of balance billing on social welfare? After restrictions on balance billing were

enacted in the USA, several theoretical papers attempted to predict the effects of this reform on

social welfare. Papers by Paringer (1980), Mitchell & Cromwell (1982), Holahan & Zuckerman

(1989) assume that physicians face a downward-sloping demand curve and do not differ in the

quality of care they provide but are able to price discriminate their patients. If physicians agree

to treat patients who pay only the regulated fee, social welfare is unchanged: balance billing

results in a transfer of surplus from patients with a high willingness to pay to physicians. More

recent papers assume that physicians are not homogeneous and discriminate between patients

in price and quality of care (Glazer & McGuire 1993, Kifmann & Roeder 2011). These authors

conclude that balance billing improves welfare because quality is higher for both regulated-

52 Chapter1

fee and balance-billed patients. A key assumption is that physicians have perfect information

about patients’ willingness to pay and are able to price discriminate perfectly. Jelovac (2013)

points out that this assumption is unrealistic. She assumes that physicians do not have perfect

information about patients’ ability to pay. On this basis, she finds that balance billing can

reduce access to care and therefore decrease social welfare.

Empirical evidence on limits to access to health care due to balance billing is rather scarce and

inconclusive. Using US data, McKnight (2007) finds that restrictions imposed on balance billing

reduced out-of-pocket payments by 9%. However, she does not find any evidence of an increase

in healthcare use, which supports the idea that balance billing acts solely as a mechanism of

surplus extraction without hindering access to care. On the other hand, a descriptive analysis

of French data indicates that healthcare use is reduced in regions where balance billing is

widespread (Despres et al. 2011).

1.3 French regulation of ambulatory care and balance billing

In France, ambulatory care is mostly provided by self-employed physicians paid on a fee-for-

service basis. Since 1980, physicians can choose between two contractual arrangements with the

regulator. If they join ’Sector 1’, physicians are not permitted to balance bill. They agree to

charge their patients the reference fee (e23 or e25 in 2012 for a routine visit to a generalist or a

specialist), and get tax deductions in return. If they join ’Sector’, they are allowed to set their

own fees. Access to Sector 2 has been closed to most GPs since 1990, so most of them are in

Sector 1: 87% in 2012. Hence balance billing concerns mostly specialists. On average, balance

billing adds 35% to the annual earnings of Sector 2 specialists. In 2012, 42% of specialists were

in Sector 2. However, this proportion varies greatly across regions and specialties: for instance,

the proportion of specialists in Sector 2 is 19% for cardiologists, 73% for surgeons and 53% for

ophthalmologists.

Patients’ out-of-pocket payment for a consultation depends on the sector of the specialists they

consult, and on their supplementary insurance coverage. Coverage of balance billing varies

between SHI contracts: statistics are not complete, but 52% of individual SHI subscribers are

1.3 French regulation of ambulatory care and balance billing 53

not covered for balance billing; in polls, 48.5% of all SHI subscribers - both individual and

occupational group subscribers - state that they are well covered for balance billing (Célant

et al. 2014).

1.3.1 The decision to consult a Sector 2 specialist

Sector 1 and Sector 2 specialists are supposed to provide the same medical service and balance

billing is supposed to amount to charging a higher price for the same thing. However, access to

Sector 2 has been restricted since 1990 to physicians who have been practicing in a qualifying

hospital setting, which suggests that they have higher level of education and of skill. Apart

from this, patients have no other information on differences in quality of care provided by

physicians. In this context, a physician’s choice to belong to Sector 2 can be seen as a signal

about skill (Spence 1973) and patients might prefer to consult a Sector 2 physician in order

to have a better chance of getting high quality care (Batifoulier & Bien 2000). Nevertheless,

beyond the issue of care quality, other potential differences between Sector 1 and 2 specialists

are observable: if there is a local shortage in Sector 1 specialists, consulting a Sector 1 specialist

exposes the patient to search costs, waiting time and transportation costs, whereas Sector 2

specialists can be more readily accessible.2

Consider a utility maximizing patient who chooses the levels of consumption of non-medical

goods (z) and of consultations of Sector 1 and Sector 2 specialists (x1 and x2) in order to

maximize U(z, h(x1,x2)) under a budget constraint. h is the level of the patient’s health, given

by a subjective health production function: h = h0 + g(x1,x2), where h0 is the level of health

without any specialist consultation. The output provided by g(x1,x2) depends on a patient’s

beliefs regarding the productivity and quality of Sector 1 and Sector 2 specialists.

Consider p the regulated fee and bb the level of balance billing. As stated earlier, all supplemen-

tary insurance contracts cover the share of the regulated fee which is not covered by NHI, i.e. 30

% for a consultation.3 In addition, some SHI contracts cover balance billing. We denote γ the

2A website of the National Health Insurance provides information on available specialists, if they belong toSector 1 or 2, and indications of their fee level.

3In France SHI contracts are allowed to cover copayments, except for a negligible copay of e1 per consultationwhich was introduced in 2004.

54 Chapter1

rate of coverage by mandatory NHI, c the minimal rate of coverage offered by all supplementary

health insurers (copayment coverage), and s the balance billing coverage offered by some SHI

contracts. The cost of access to Sector 1 or 2 specialists is also influenced by their availability.

We denote d1 and d2 search costs, as well as transportation and waiting time costs associated to

access to a Sector 1 or a Sector 2 specialist. d1 and d2 are linked to local specialist : population

ratios.

Hence, the total cost of a consultation of a Sector 1 specialist is as follows: p1 = p(1−γ −c)+d1;

and the total cost of a consultation of a Sector 2 specialist is p2 = p(1−γ−c)+(bb−s)+d2. Given

that all individuals in our sample are fully covered for co-payments4, p(1 − γ − c) ≃ 0. The

relative price of a Sector 2 consultation is given by5:

p2

p1=

(bb − s) + d2

d1(1.1)

Given this formalization, the decision to consult a Sector 2 specialist is based on cost mini-

mization for a given level of health production g(x1,x2) = h − h0. If the patient believes that

consultations of a Sector 1 and Sector 2 physician are not perfectly substitutable, the isoquants

of the health production function are not linear. Given that the iso-cost lines have a slope equal

to the relative pricep2

p1, an increase in balance billing coverage (say, from s = 0 to s > 0)

induces an increase in the use of Sector 2 physicians. The magnitude of the impact depends on

the availability of Sector 1 physicians. Indeed, the variation of the relative price with respect

to s is∂ p2

p1

∂s= −

1d1

.

Note that when Sector 2 physicians are very scarce,p2

p1→ ∞ whatever the value of s: in this

situation, a change in SHI coverage should have no effect on recourse to Sector 2 physicians.

Another specific case is when the patient believes that Sector 1 and Sector 2 physicians are

perfectly substitutable: this leads to corner equilibria, with only Sector 1 or only Sector 2

consultations, depending on the value ofp2

p1and on g(.) parametrization.

4Except for the negligible e1 copay.5Given that most contracts impose a ceiling on balance billing coverage, s is not a coverage rate (it is fixed

and not proportional to balance billing), but this does not affect the model’s predictions.

1.4 Data and empirical strategy 55

1.3.2 Availability of Sector 1 and Sector 2 specialists

As stated previously, supply organization can influence recourse to Sector 2 specialists. Fig-

ure 1.1 provides geographical information about the specialist : population ratio of Sector 1

and Sector 2 specialists for the 95 départements of continental France. The specialist : pop-

ulation ratio is an indicator of physicians’ availability, i.e. search, transportation and waiting

time costs associated to access to a Sector 1 or a Sector 2 specialist. Medical density is used

here as an indicator of distance (in the geographical and time sense) to the doctor. We are not

interested in using a concentration index for comparing market power of Sector 1 versus Sector

2 specialists because what is important in our analysis is to measure the distance for patients

to any single doctor of each type. Of course the specialist : population ratio is an imperfect

indicator because there are border effects and geographical areas do not coincide with practice

areas.

Figure 1.1 shows that there is not always an inverse relation between specialist : population

ratios for Sectors 1 and 2 specialists: on the Mediterranean cost, both types of specialists

are numerous. Conversely, in Brittany (the North-West of France), there are many Sector 1

specialists and very few Sector 2 specialists. The Parisian region, on the other hand, has many

Sector 2 specialists and very few Sector 1 specialists. Figure 1.2 gives the proportion of Sector

2 specialist consultations and average balance billing per consultation for each département, as

computed on our sample. The comparison with Figure 1.1 suggests a strong impact of supply

side drivers on both propensity to see a Sector 2 specialist and the amount of balance billing.

1.4 Data and empirical strategy

We use a panel data set from a French supplementary insurer: Mutuelle Générale de l’Education

Nationale (MGEN). For historical reasons, MGEN processes claims from NHI in addition to

offering supplementary insurance (MGEN-SHI). Our data stemmed from administrative MGEN

data: they provide, for each policyholder, detailed information about medical bills and reim-

bursements for both national and supplementary insurance.

56 Chapter1

MGEN is a mutuelle, i.e. a non profit insurer which administrates mandatory health insurance

for teachers and ministry of education employees. Most of them are civil servants. MGEN also

supplies supplementary health insurance in the form of a single contract which offers minimal

coverage: it covers co-payments but not balance billing. The premium is defined as a pro-

portion of wages for working members and of pensions for retirees. People subscribe to this

supplementary insurance on a voluntary basis. The fact that its premiums are proportional to

wages gives MGEN an odd position in the SHI market. Most supplementary insurers charge

a premium that does not depend on wage or income. In the short term, young, healthy and

wealthy teachers should be better off purchasing coverage with a premium that depends on age.

However, the MGEN-SHI contract becomes more valuable as individuals grow older. In order

to avoid free riding, MGEN-SHI penalizes late entry and does not allow members who leave to

return later on. Currently, MGEN processes NHI claims for 3.3 million individuals (all teachers

and ministry of education employees, their families and pensioners). Among them, 2.3 million

subscribe to the MGEN-SHI contract.

1.4.1 Empirical strategy

Our empirical strategy is based on MGEN-SHI enrollees who switched to other supplementary

insurers during our observation period. Since MGEN-SHI covers only co-payments, i.e. the

minimal coverage offered by supplementary health insurers, we can assume that this switch

entails equal or better coverage.

From the MGEN database, we built two samples over the period 2010-2012: one with 87,291

’stayers’, the other one with 7,940 ’switchers’. The former remained MGEN-SHI enrollees over

the observation period (2010-2012), the latter was MGEN-SHI subscribers in January 2010, but

terminated their contracts in 2011. Because MGEN still processes their NHI claims in 2012,

we observe their health expenditures over the whole period. Switchers’ decision to leave in

2011 creates a positive shock on their insurance coverage. Therefore, we can use Stayers and

Switchers as control and treatment groups (Figure 1.3).

We do not observe switchers’ coverage for balance billing after they have left MGEN-SHI.

However, since MGEN-SHI coverage of balance billing is zero, we know that their new coverage


will be at least as good as, and probably better than the MGEN-SHI coverage. Hence our

estimated impacts should be interpreted as ’intent-to-treat’ (ITT) effects. These are likely to

understate the real impact of better insurance coverage and should be interpreted as lower

bounds.

The original sample was composed of 91,629 stayers and 8,249 switchers. For the purpose of

the study, we decided to over-represent switchers: in our data the proportion of switchers is not

representative of the actual switching rate of 0.5%. We excluded the people who live outside

continental France (territories such as Guadeloupe, Martinique, and so on) and the top 1% of

care users in 2010 or 2012 (more than 28 consultations a year for stayers, 30 for switchers). As

stated above, balance billing is not an issue for GPs, so we focus on specialists. More precisely,

we measure the effect of insurance coverage on the decision to visit a specialist who balance

bills, conditional on consulting a specialist. Therefore, we restricted the sample to individuals

who consulted a specialist at least once in 2010 and in 2012 (spe = 1). They represent 45%

of stayers and 48% of switchers. To sum up we use a sample of 43,111 individuals: 39,292 are

stayers and 3,819 switchers; they are observed from 2010 to 2012 and consulted a specialist at

least once in 2010 and in 2012.

1.4.2 Variables

Our data provide information at the individual level about the total number of specialist con-

sultations (denoted Q), the number of consultations of Sector 2 specialists (Q2) and the total

amount of balance billing (BB). Our variables of interest are the number of specialist consul-

tations Q, the proportion of consultations of Sector 2 specialists Q2/Q, average balance billing

per consultation BB/Q and average balance billing per Sector 2 consultation BB/Q2 (the last

indicator is computed for individuals with at least one visit to a Sector 2 specialist (Spe2 = 1)).

Using these four indicators allows us to distinguish between patients’ use of specialists, patients’

decisions to consult a Sector 2 specialist, and the amount of balance billing. Of course, the

average amount of balance billing per Sector 1 or 2 consultation (BB/Q) is influenced both by

the proportion of Sector 2 consultations and, on the supply side, by BB/Q2 the prices set by

Sector 2 specialists.

58 Chapter1

At the individual level, we can only compute average balance billing. Indeed, our data provides

information on the number of consultations for each specialty in Sector 1 and Sector 2 but not

on the fee associated with each consultation. However, we can take advantage of the specialties

needed by patients to control for the extent of their choice of Sector 1 or 2 specialists. In France,

gynecologists, ophthalmologists, surgeons and ENT6 specialists balance bill in a much larger

proportion than their colleagues. As a result, it is more difficult to avoid a Sector 2 physician

for a patient who needs to consult one of these types of specialists, inducing more balance

billing per consultation. To deal with this heterogeneity, we introduce a dummy variable for

"expensive physicians" (Exp.Phy), which is equal to 1 when the individual sees at least one of

these specialists.

Demand characteristics include gender, age, income and health status. Our income variable

is based on the individual’s wage. It is computed using the fact that MGEN-SHI premiums

are proportional to individuals’ wages. Because premiums are limited by lower and upper

bounds for monthly wages lower than e1,000 and higher than e4,900, this proxy is close to

a truncated individual wage. As concerns health status, we know if the patient has a chronic

disease (CD = 1). Supply side characteristics include visits to a GP, specialist : population

ratios and the Exp.Phy dummy variable. In France, one can consult a specialist without

seeing a GP beforehand. Patients do not need their GP’s agreement to consult gynecologists or

ophthalmologists. For other specialties, GPs are gatekeepers and their consent determines the

extent of NHI reimbursement.7 We control for this arrangement with a dummy indicating that

the patient consulted a GP at least once in the current year. Supply side organization is taken

into account using information provided by the NHI8 about specialist : population ratios at

the département level in Sector 1 (SPR1) and 2 (SPR2). We introduce an interaction between

Sector 1 and 2 specialist : population ratios to allow for non linear effects.

6Ear, nose and throat specialists.7Reimbursements are reduced in case of recourse to a specialist without a GP’s referral and incentives are

given to SHI to not cover this penalty.8SNIR (Syndicat National Inter Régimes), provided by CNAMTS (Caisse Nationale d’Assurance Maladie des

Travailleurs Salariés)


1.4.3 Basic features of the data

Because MGEN enrollees are mostly teachers, the sample is not representative of the French

population (Table 1.1). There are many women (65%), their average age is 55, and the average

monthly wage is e2434 , which is higher than the average wage in France. We warn against

generalizing our results to different settings, because we are dealing with a population which is

likely to have specific habits concerning health, specific values and a particular degree of risk

aversion.

Most studies of competition in health insurance find a higher propensity of young, healthy and

highly educated individuals to switch companies (Dormont et al. 2009). We find the same

characteristics for people who decided to leave MGEN-SHI: they are much younger (42.5 versus

55.4) and healthier than stayers (only 6.8% have a chronic disease, versus 17.5%). However,

our switchers have a lower income than stayers. This is because wage variability is reduced

for teachers in comparison with the whole population; moreover, teachers’ wages are strongly

correlated with age because promotions are mostly based on seniority. Here, switchers have a

lower income partly because they are thirteen years younger than stayers on average.

Table 1.2 displays statistics about recourse to specialists, proportion of Sector 2 consultations

and amount of balance billing for stayers and switchers in 2010, when both groups had no

coverage for balance billing. These statistics depict heterogeneity in preferences and situations

for individuals with the same coverage. On average, stayers and switchers consulted specialists

respectively 3 and 3.2 times in 2010. The proportion of Sector 2 consultations is significantly

higher for switchers than for stayers: 51.6% versus 44.6%. As a result, switchers pay significantly

more balance billing in total (e41 versus e30 ) and per consultation (e12.8 versus e10.2 ). So,

even when they had no coverage for balance billing, switchers consulted Sector 2 specialists

more often and paid more balance billing than stayers.

The second column of Table 1.2 gives the mean and standard deviations for observations that

are higher than the 99 percentile (average of the top 1%) for each indicator. The top 1%

average values of balance billing show that, even with a SHI contract, individuals are not

60 Chapter1

protected against high out-of-pocket expenditures: e433 per year for stayers and e505 per year

for switchers.9

The two last columns of Table 1.2 display mean and standard deviations computed for indi-

viduals living in areas characterized by low or high levels of Sector 2 specialist : population

ratio. We find a strong influence of supply side organization: differences between stayers and

switchers are significant only in places with many Sector 2 specialists (last column).

1.5 Econometric specification and estimation

The causal impact of a positive coverage shock on our variables of interest can be identified by

estimating a model with individual fixed effects on the panel obtained by pooling years 2010 and

2012. To compare switchers and stayers, we include in the regressors a dummy variable named

QUIT which represents leaving MGEN-SHI in 2011 (QUIT = 1 for Switchers in 2012, = 0 in

2010). We also include a dummy variable for the year 2012 (I2012 = 1 for t = 2012, I2012 = 0 for

t = 2010) to allow for a possible trend that would induce changes in behavior for both switchers

and stayers. We also control for time varying demand and supply variables denoted Xit and Sit.

Vector Xit includes variables recorded at the individual level: income, chronic disease and GP

consultation. Sit is a vector of regressors relative to supply organization: specialist : population

ratios for Sector 1 and Sector 2 in the département where the patient lives, and the dummy

variable indicating the patient’s need for expensive physicians Exp.Phy.

Yit = β0 + τQUITit + λI2012,t + β1Xit + β2Sit + αi + ǫit, t = 2010,2012 , (1.2)

Yit denotes the dependent variable, which is one of the four indicators of interest: log(Q),

log(Q2/Q), log(BB/Q) and log(BB/Q2). We introduce individual fixed effects αi. The distur-

bance εit is supposed to be iid (0,σ2ε).

Specifying a fixed effect αi allows for potential nonexogeneity of the decision to leave MGEN-

SHI if this decision were correlated with individual unobserved heterogeneity. These effects9This is especially true because these figures are computed on a sample where the top 1% of care users have

already been excluded: on the whole sample, we find average annual balance billing for the top 1% of care usersequal to e638 for stayers and e914 for switchers.

1.5 Econometric specification and estimation 61

are likely to be connected to switchers’ permanent belief in better quality of care in Sector

2, or specific tastes that would induce higher disutility of time consuming travel and search

efforts. The decision to leave MGEN-SHI might also be induced by a transitory shock in health

care needs (the onset of illness which we cannot observe perfectly, although we observe and

control for the onset of chronic disease) or by an information shock that affects beliefs regarding

quality of care in Sector 2. In this case, there is a correlation between ǫit and the decision

to leave MGEN-SHI. For this reason, we have performed an instrumental variable estimation

of equation (1.2), in order to obtain a consistent estimation of the causal impact of improved

coverage on Yit.

A reliable instrument must be correlated with the decision to leave MGEN-SHI (QUIT ) and

must not directly affect the dependent variable Yit. We have at our disposal two variables

that are good candidates to be relevant instruments, and appeared to be exogenous and well

correlated with QUIT . We used the decision to retire in 2011 for people younger than 55 and

a change of département of residence in 2011. The threshold chosen for retirement age refers

to a specific right for public school teachers and other civil servants that allowed those who

raised three or more children to retire before they were 55.10 This right was revoked recently

and eligible teachers had to use this opportunity before January 2012. This retirement policy

change created an exogenous shock that gives us a good instrument. As shown in Figure A1 (in

the online appendix), a large number of teachers retired in 2011 before they were 55 (300 in our

sample) and half of them decided to leave MGEN-SHI the same year. MGEN pricing rules raise

premiums from 2.97% of wages before retirement to 3.56% of pensions after. This shock on

premiums can encourage people to switch, irrespective of any shock on care needs or beliefs in

the quality of care in Sector 2. We also use the decision to move from one département to another

in 2011 as an instrument for the decision to leave MGEN-SHI.11 Because MGEN has separate

agencies in each département, MGEN-SHI policy holders who move to a new département face

high administrative costs in order to transfer their records to a new agency. Individuals who

hesitated to switch before moving because of switching costs, may decide to switch upon moving

because they face administrative costs in any case.10Civil servants who raised three children or more were eligible for early retirement if they had worked in the

civil service at least 15 years.11In our sample, 1,415 individuals decided to move from one département to another in 2011, of which 287

decided to leave MGEN-SHI the same year.

62 Chapter1

Even though it was encouraged by an exogenous policy change, early retirement might be

linked with a negative health shock. To address this concern, we checked that individuals who

retired before 55 in 2011 were not different in 2010 from those who remained active, as regards

chronic disease, GP and specialist consultations, as well as drug consumption (Table AI in

the appendix). We also found that future movers were not different in 2010 from non-movers

either. Another difficulty arises if exogenous incentives to switch because of early retirement or

département change are concomitant with a health shock. To rule out this possible source of

bias, we checked if our compliers experienced any shock in their number of GP consultations

and drug consumption between 2010 and 2012. Indeed, because MGEN-SHI fully covers co-

payments for GP visits and drugs, a shock on SHI coverage together with no change in health

care needs should induce no change in recourse to GPs or drug consumption. Results displayed

in Table AII show that we have not found any significant change between 2010 and 2012 in use

of GPs or drugs for switchers who moved or took early retirement. Conversely, a negative health

shock should increase both GP visits and drug consumption. Hence the strong impact of the

onset of a chronic disease on the number of GP consultations (+13%) and drugs consumption

(+64%), see Table AII.

1.6 Results

Our results are displayed in Tables 1.3 and 1.4. Table 1.3 gives the estimates of the causal

impact of better coverage on the four indicators Yit. Table 1.4 presents the estimations for the

other regressors and individual fixed effects.

Several tests support the consistency of our instrumental variable estimates. Sargan tests all

lead to non rejection of instrument compatibility.12 In addition, we examined whether our

estimations could be subject to the weak instrument problem. For this purpose, we tested

for the significance of the excluded instruments in first stage regressions. We found a large

significance of the partial correlation between the excluded instrument and QUIT , with high

F statistics (larger than 92, see Table AIII in the appendix). Following Bound, Jaeger and

12For dependent variables log(Q), log(Q2/Q), log(BB/Q) and log(BB/Q2), we obtain very small values forthe Sargan statistic, with p-values that are equal, respectively, to 0.94, 0.85, 0.71 and 0.10. We obtain similarresults when we split the sample into sub-samples relative to different levels of SPR1.

1.6 Results 63

Baker (1995), this suggests that we can rule out instrument weakness. We rely on IV results

when Hausman tests lead to rejection of QUIT exogeneity. Otherwise we can rely on OLS

estimates, which are consistent with IV estimates when QUIT is exogenous. All estimations

include individual fixed effects.

1.6.1 The impact of better coverage on the use of Sector 2 specialists and

balance billing

Table 1.3 provides the OLS and IV estimates of the impact τ of the coverage shock for the whole

sample (1) and various sub-samples (2-4), on the use of specialists, the proportion of Sector 2

consultations and the amount of balance billing per consultation. For each sub-sample and each

dependent variable we also provide the Hausman test p-value. As stated previously, we control

for unobservable individual heterogeneity and potential non-exogeneity of QUIT . Note that

a more simple difference-in-differences approach comparing stayers and switchers in 2010 and

2012 led to results that were similar to our fixed effect OLS estimates.

For the whole sample (1), better coverage has no impact on the use of specialists (log(Q))

but increases the share of Sector 2 consultations by 9%, which results in a 32% increase in

the amount of balance billing per consultation. Hence, because it raises demand for Sector 2

physicians, better coverage by supplementary health insurance is likely to encourage the rise

in medical prices. However, we do not find a significant effect of better coverage on the price

of Sector 2 consultations (log(BB/Q2)): patients who normally visit S2 specialists do not take

advantage of their better coverage to see even more expensive physicians. This also suggests

that physicians do not adjust their prices to their patients’ coverage, at least in the short run.

As concerns significant coefficients, we find 2SLS estimates that are larger than the OLS esti-

mates (see, for instance, Table 1.3, (1)). At first glance, it seems surprising to find a negative

endogeneity bias, given that people presumably switch insurers to enjoy better coverage for bal-

ance billing. In fact, such a negative bias is quite possible: given that our specification allows for

an individual fixed effect, the IV estimation mostly corrects bias due to transitory health shocks.

These shocks can be positively or negatively correlated over time, but a negative correlation is

more likely because the onset of a chronic disease is already captured through a dummy variable

64 Chapter1

in the regressors. Let us take the example of a tibia fracture in 2010. The patient experiences

many consultations with large balance billing and she decides to quit MGEN-SHI in 2011 to

get better coverage. In 2012, her need for Sector 2 specialist consultations is lower because she

has recovered (however, our IV estimates show that, for a given level of needs, she uses more

Sector 2 specialists than before quitting, because of the improvement in coverage).13

1.6.2 The effect of supply side organization on the impact of better coverage

As shown in Figure 1.1, local availability of Sector 1 specialists varies dramatically across

geographical areas (départements). This is likely to induce heterogeneity in the impact τ of

better coverage because the relative price of a Sector 2 consultation is not only influenced by

balance billing coverage s, but also by search and transportation costs d1 and d2 to reach a

Sector 1 or 2 specialist. Because p2

p1= (bb−s)+d2

d1, one has

∂p2

p1

∂s = − 1d1

, suggesting that the impact

of a coverage shock depends on the availability of Sector 1 specialists. Precisely, assuming

that search costs, transportation costs and waiting time decrease with the number of Sector 1

specialists, the impact of insurance coverage should be higher in regions where the number of

Sector 1 specialists is relatively low.

To investigate this, we split the sample into two sub-samples,14 one with areas with high Sector

1 specialist : population ratios (SPR1), the other with medium and low levels. The results

are striking: when Sector 1 specialists are numerous (Table 1.3, (2)), a coverage shock has no

impact on the use Sector 2 specialists and balance billing. In other words, when patients have a13A simple model enables us to compute the bias. For individual i, denoting the year by t = 10,11 or 12, we

have:bbi,10 = vi

quiti,11 = a bbi,10 + ui + εi,11 + ξi,11

bbi,12 = τ quiti,11 + vi + ηi,12

where bb is the use of balance billing and quit is the decision to quit in 2011. Formally, the model above removes allcontrol variables (density levels, income, chronic disease indicator, etc.) by taking the residuals of the projectionsof balance billing and quit on these control variables (Frish-Waugh theorem). vi (respectively, ui) is an individualfixed effect referring to the disutility of transportation costs for i (respectively, to i′s risk aversion). ui and vi aresupposed to be uncorrelated. ε and η are transitory health shocks influencing the decision to quit and the use ofspecialists who balance bill their patients. ξ is the transitory policy shock related to the repeal after 2011 of thepossibility to retire before 55. ξ is supposed to be uncorrelated with v, ε and η. Denoting τols the OLS estimator

of τ , one has: p lim τols = τ + aσ2

v

σ2q

+ σεη

σ2q

, where σ2

v and σ2

q denote the variances of v and quit , and σεη denotes

the covariance between εi,11 and ηi,12. In fixed effect estimations, vi is removed from the specification and theasymptotic bias becomes: p lim τols,F E = τ + σεη

σ2q

. It has the same sign as σεη, which can be positive or negative.14We have performed estimations allowing coefficient τ to vary across local proportions of sector 1 specialists.

These estimations provide coefficients that are similar in magnitude and precision to what we obtain whensplitting our sample into various sub-samples, as presented in this section.

1.6 Results 65

genuine choice, we do not find evidence of moral hazard. Conversely, when Sector 1 specialists

are scarce (Table 1.3, (3)), we find larger impacts: better coverage yields a 14% increase in the

proportion of consultations of Sector 2 specialists, and a 47% increase in the average amount

of balance billing per consultation.

Finally, we find evidence of limits in access to care on a sub-sample (Table 1.3, (4)) restricted

to areas where Sector 1 specialists are scarce. This is the only case where we find that better

coverage induces a significant rise in the quantity of specialist consultations Q (+ 42%), in

addition to impacts on the share of Sector 2 consultations and on average balance billing per

consultation. This result suggests that the lack of Sector 1 specialists in these areas creates a

shortage in affordable care, leading some individuals to give up on specialist consultations. This

evidence of limits in access to care concerns a sizeable minority of individuals in our sample

(30%).

1.6.3 Other determinants of balance billing

We now focus on the respective effects, ceteris paribus, of supply side organization, income and

chronic diseases on specialist visits, use of Sector 2 specialists and average amount of balance

billing per Sector 2 consultation. Table 1.4 presents the estimates of parameters λ, β1 and

β2 resulting from OLS applied to equation 1.2 with fixed effects, for the four indicators Yit.

For these coefficients, magnitude and significance of 2SLS estimates are similar. Table 1.4 also

displays the OLS estimates of dummy Switcheri, equal to 1 if individual i quits MGEN-SHI in

2011 on estimated fixed effects obtained in the panel data estimation.

On our reduced form, the impact of medical density results, on the demand side, from distance

to Sector 1 or 2 specialists and, on the supply side, from the process of price setting by Sector 2

specialists. We find that a higher proportion of Sector 2 specialists at the local level leads to an

increase in the price of Sector 2 consultations, with a reduced impact if there are many Sector 1

specialists. An increase from 15 (Low SPR2) to 25 (High SPR2) Sector 2 specialists per 100,000

inhabitants increases the average price of a Sector 2 visit by 5% in Low SPR1 but only by

1.6% in High SPR1. Given that the proportion of Sector 2 specialists is especially high (above

50%) for gynecologists, surgeons, ophthalmologists or ENT specialists, patients who need to

66 Chapter1

consult one of these specialists have little choice. Our estimates show that a visit to one of

these specialists increases the average amount of balance billing per consultation by 79%.

Other determinants such as income or health status do not affect the consumption of balance

billing. An increase in income does not change the use of Sector 2 specialists.15 However, we

find a significant impact on the total number of visits to a specialist: a 10% increase in income

increases the annual number of visits by 1.6%. Individuals with greater health care needs do

not change their use of Sector 2 specialists either. Indeed, patients who suffer from a chronic

disease are likely to increase the number of visits by 19% but do not change their proportion of

Sector 2 visits.

Demand for Sector 2 consultations can also be explained by unobservable individual preferences

(beliefs in Sector 2 quality, desire to avoid waiting lists). Actually, we find evidence of individual

heterogeneity between stayers and switchers. To do so, we regress the dummy Switcheri on the

estimated individual fixed effects obtained in the panel data estimation. Obviously, with a 2-

year panel, we cannot expect our estimates of αi to be consistent. Nevertheless, it is interesting

to examine the correlation between these estimates and recourse to Sector 2 specialists. We find

that the average amount of balance billing per visit is 21% higher for switchers than for stayers.

Regardless of their insurance coverage, switchers visit Sector 2 specialists more often (the share

of Sector 2 is 4% higher for switchers) and those specialists charge them higher fees (+8%). So,

we find that switchers, i.e. people who seek better coverage, have also a higher utilization of

Sector 2 specialists.

1.6.4 Robustness checks

Given the exogenous shock on retirement rules in 2011, ’early retiree in 2011’ is a very convincing

instrument. Unfortunately, if we use it as the only excluded instrument for QUIT, we end up

with a relatively small number of compliers. In order to increase our estimators’ precision we use

it together with the instrument ’move in 2011’. In Table AIV (in the appendix), we show that

most results remain similar in magnitude when using only the ’early retiree in 2011’ instrument.

15Because our specification entails fixed effects, the estimated impact of income here measures the effect ofa change in income for a given individual. Actually, the level of income is positively correlated with the use ofbalance billing: between individuals, the fixed effects are significantly correlated with income levels.

1.7 Conclusion 67

However, the result on the quantity of consultations in Low SPR1 seems mainly driven by the

people who move in 2011.

Our results are also very robust to a change in the definition of SPR1 categories. We checked

that results do not change when using the median to split our sample. Results are also robust

when we exclude areas where there are very few Sector 2 specialists from the sample (see Table

AV in the appendix). Indeed, when the number of Sector 2 specialists is very low, having better

coverage for balance billing does not have any effect, because people do not have access to a

Sector 2 specialist in any case. Our estimations confirm this idea but we decided not to present

this result because the number of switchers in these areas is too small.

1.7 Conclusion

In this paper we evaluate the causal impact of an improvement in health insurance coverage on

the use of specialists who balance bill. We use panel data to control for unobservable individual

heterogeneity and rely on instrumental variable methods to deal with possible non-exogeneity

of the decision to switch to an insurer that offers better coverage for balance billing.

In France, the use of Sector 2 specialists (who balance bill) can be due to a belief that they

provide better quality of care, or to difficulties in gaining access to other doctors, i.e. Sector

1 specialists, who do not balance bill. If the latter is not numerous, patients face search costs,

waiting time and transportation costs in order to consult a specialist who does not charge more

than the regulated fee. As a matter of fact, we find a large heterogeneity between individuals in

the propensity to use Sector 2 specialists. In particular, people who decided to leave MGEN-SHI,

i.e. switchers, are more likely to consult Sector 2 specialists, ceteris paribus.

Our estimations show that better coverage increases the demand for specialists who balance bill.

On the whole sample, we find that better coverage leads individuals to raise their proportion

of consultations of specialists who balance bill by 9%, which results in a 32% increase in the

amount of balance billing per consultation. However, the effect of health insurance clearly

depends on supply side organization. We find no evidence of any impact of a coverage shock on

68 Chapter1

the use of Sector 2 specialists in areas where there are many Sector 1 specialists. About 42% of

the sample live in these areas and therefore would not increase their use of expensive physicians

if their coverage for balance billing improved.

On the contrary, when Sector 1 specialists are scarce, a coverage shock has a strong impact:

individuals raise their proportion of consultations of Sector 2 specialists by 14%, which results in

a 47% rise in the amount of balance billing per consultation (this concerns 58% of the sample).

In addition, we find evidence of limits in access to care due to balance billing in areas where

Sector 1 specialists are scarce. Indeed, better coverage enables people living in these areas

to increase their number of consultations. Evidence of such limitation concerns 30% of our

sample, a sizeable minority. Given that low-income individuals are under-represented in our

sample which consists mostly of teachers, our estimated effect of better coverage on access to

specialist care should be interpreted as a lower-bound. Consequently, this result suggests that

balance billing is likely to induce non-negligible limits in access to specialists in France.

Our results enable us to deal with current policy questions regarding regulation of balance

billing and SHI. We have found that generous supplementary coverage can contribute to a rise

in medical prices by increasing the demand for specialists who balance bill. However, this

inflationary impact appears only when few specialists charge the regulated fee. When people

can choose between physicians who balance bill and physicians who do not, a coverage shock has

no impact. When the number of specialists who charge the regulated fee is sufficiently high (e.g.,

more than 52 specialists for 100,000 inhabitants), there is no evidence of limits in access to care,

or of an inflationary effect of supplementary coverage. In consequence, the most appropriate

policy to guarantee access to care while containing the price of care is to monitor supply in order

to give patients a genuine choice of physicians. Furthermore, we have found heterogeneity in

preferences such that some individuals prefer to consult specialists who balance bill. Hence, this

policy allows for an improvement in welfare through insurance contracts offering balance billing

coverage for those who want it. However, if policy makers are not able to ensure a sufficient

supply of specialists who charge the regulated fee, limiting insurance coverage can be a second

best solution to contain the increase in medical prices.

Tables and Figures 69

Tables and Figures

Figure 1.1 – Specialist:population ratio at the département level for Sector 1 and Sector 2specialists in 2010

Source: SNIR data Source: SNIR data

Figure 1.2 – Share of consultations of Sector 2 specialist (Q2/Q) and average balance billingper Sector 2 consultation (BB/Q2) in 2010

Source: MGEN sample, N=58,336 Source: MGEN sample, N=34,536

70 Chapter1

Figure 1.3 – Control and treatment groups

Table 1.1 – Number of Stayers and Switchers and individual characteristics in 2010

Whole sample if Spe=1 if Spe2=1 Women Age Income CDN N N % mean (sd) mean (sd) %

Stayers 87,291 39,292 17,848 65 55.4 (15.3) 2434 (774) 17.5Switchers 7,940 3,819 2,101 71 ∗∗∗ 42.5ˆ(13) 2399 ∗∗∗ (770) 6.8 ∗∗∗

CD: Chronic Disease∗∗∗ Significantly different from Stayers, p<0.01


Table 1.2 – Number of specialist visits and amount of balance billing in euros in 2010

Whole sample Last centile† Low SPR2 High SPR2mean (sd) mean (sd) mean (sd) mean (sd)

Q Stayers 3 (3.2) 21.4 (2.7) 2.6 (2.7) 3.2 (3.5)if Spe=1 in 2010 Switchers 3.2 ∗∗∗ (3.4) 22 (3.1) 2.7 (2.8) 3.4 ∗∗ (3.6)

Q2 Stayers 1.3 (2.0) 14 (4.2) 0.6 (1.3) 1.6 (2.3)if Spe=1 in 2010 Switchers 1.6 ∗∗∗ (2.4) 15.5 ∗∗∗ (3.5) 0.7 (1.5) 1.9 ∗∗∗ (2.6)

Q2/Q Stayers 44.6% (0.44) 100% ♭ (0.00) 25.2% (0.38) 53.4% (0.43)if Spe=1 in 2010 Switchers 51.6% ∗∗∗ (0.44) 100% (0.00) 28% (0.40) 60% ∗∗∗ (0.42)

BB Stayers 30 (58.9) 433 (184) 11.5 (31.2) 42 (74)if Spe=1 in 2010 Switchers 41 ∗∗∗(72.8) 505 ∗∗∗ (164) 13 (26.7) 53.6 ∗∗∗ (85.5)

BB/Q Stayers 10.2 (12.5) 62 (14.7) 4.6 (8.5) 13.5 (13.9)if Spe=1 in 2010 Switchers 12.8 ∗∗∗ (13.6) 65 (10.8) 5.1 (8.7) 16 ∗∗∗ (14.5)

BB/Q2 Stayers 22 (11.5) 76.8 (17.2) 18 (10.2) 25 (12)if Spe2=1 in 2010 Switchers 24 ∗∗∗ (11.8) 76 (11.3) 18 (10) 26 ∗∗∗ (12)∗∗∗ Significantly different from Stayers, p<0.01∗∗ Significantly different from Stayers, p<0.05

MGEN sample: 58,336 individuals with at least one specialist consultation in 2010

BB/Q2: subsample of 34,536 individuals with at least one S2 specialist consultation in 2010

† Highest percentile for each variable.

♭ 32% of stayers and 37% of switchers visited exclusively S2 specialists hence Q2/Q = 100%

SPR2 : Sector 2 specialist:population ratio

Low SPR2 : départements where SPR2 is under 12 per 100,000 inhabitants (first quartile of SPR2)

High SPR2 : départements where SPR2 is above 29 per 100,000 inhabitants (last quartile of SPR2)

72 Chapter1

Table 1.3 – Impact of better coverage on visits to a specialist, use of Sector 2 specialists andaverage amounts of balance billing

Estimations with individual fixed effects, T=2010,2012N % log(Q) log(Q2/Q) log(BB/Q) log(BB/Q2)

(1) Whole sample / OLS 43,111 100% -0.02 0.01 0.03 -0.00(0.02) (0.01) (0.02) (0.01)

Whole sample / 2SLS 0.12 0.09** 0.32* -0.16(0.12) (0.04) (0.18) (0.10)

[Hausman test p-value] [0.24] [0.04] [0.12] [0.10]

(2) High SPR1 / OLS 17,893 41.5% -0.03 0.01 0.05 0.01(0.03) (0.01) (0.04) (0.02)

High SPR1 / 2SLS -0.05 0.05 0.13 -0.23(0.25) (0.08) (0.39) (0.19)


(3) Low & Med. SPR1 / OLS 25,218 58.5% -0.03 0.00 0.01 -0.00(0.02) (0.01) (0.03) (0.01)

Low & Med. SPR1 / 2SLS 0.23 0.14*** 0.47** -0.06(0.14) (0.05) (0.22) (0.11)


(4) Low SPR1 / OLS 12,915 30% 0.00 0.01 0.04 -0.02(0.02) (0.01) (0.04) (0.02)

Low SPR1 / 2SLS 0.42** 0.14** 0.61** 0.08(0.20) (0.07) (0.31) (0.14)


MGEN sample: 43,111 individuals with at least one specialist consultation in 2010 and 2012

log(BB/Q2): subsample of 19,949 individuals with at least one S2 specialist consultation in 2010 and 2012

Other regressors: 2012, income, CD, GP, specialist:population ratio, exp.phy.

Instruments: "early retirees"; "movers"

Standard errors are shown in brackets ()

Hausman test: H0: QUIT may be treated as exogenous

SPR1: S1 Specialist:population ratio

High SPR1: départements where SPR1 is above 52 per 100,000 inhabitants (last third of SPR1)

Med. SPR1: départements where SPR1 ranges from 41 to 52 per 100,000 inhabitants (second third of SPR1)

Low SPR1: départements where SPR1 is under 41 per 100,000 inhabitants (first third of SPR1)

* p<0.1, ** p<0.05, *** p<0.01


Table 1.4 – Effect of demand and supply side drivers on visits to a specialist, use of Sector 2specialists and average amounts of balance billing

OLS Estimations with individual fixed effects, T=2010,2012log(Q) log(Q2/Q) log(BB/Q) log(BB/Q2)

2012 -0.00 (0.01) -0.01*** (0.00) -0.02** (0.01) 0.05*** (0.00)

Chronic Disease 0.19*** (0.02) -0.01 (0.01) -0.01 (0.03) -0.00 (0.02)GP -0.04*** (0.01) 0.02*** (0.00) 0.11*** (0.02) 0.01 (0.01)

log(Income) 0.16*** (0.03) 0.01 (0.01) 0.07 (0.05) -0.00 (0.03)

log(SPR1) -0.03 (0.21) 0.03 (0.07) 0.29 (0.33) 0.31 (0.20)log(SPR2) -0.02 (0.24) 0.15* (0.08) 0.87** (0.37) 0.47** (0.22)log(SPR1)*log(SPR2) 0.00 (0.06) -0.03 (0.02) -0.18* (0.09) -0.11* (0.06)Exp.phy. 0.26*** (0.01) 0.13*** (0.00) 0.79*** (0.01) 0.19*** (0.01)

Estimated fixed effect

Stayer ref. ref. ref. ref.Switcher 0.05*** (0.01) 0.04*** (0.00) 0.21*** (0.02) 0.08*** (0.01)

N 43,111 43,111 43,111 19,949


log(BB/Q2): sub-sample of 19,949 individuals with at least one S2 specialist consultation in 2010 and 2012

Other regressor: QUIT

SPR1: S1 Specialist:population ratio ; SPR2: S2 Specialist:population ratio

Magnitude and significancy of all coefficients remain the same with 2SLS estimation

For estimated fixed effect, second step standard errors are used for the test

* p<0.1, ** p<0.05, *** p<0.01

74 Chapter1

Appendix

Figure 1.4 – Number of MGEN enrollees who retired in 2010, 2011 and 2012, by age

Appendix 75

Table 1.5 – Characteristics of "early retirees" and "movers" in 2010 (Probit estimations)

(A) Early retirees (B) MoversCoeff Coeff

Chronic Disease -0.02 (0.09) 0.06 (0.04)Log(GP visits) -0.02 (0.04) 0.02 (0.02)Log(Spe visits) -0.01 (0.03) 0.03 (0.03)Log(Drugs) 0.01 (0.02) -0.02* (0.01)

N 12,861 43,111

* p<0.1, ** p<0.05, *** p<0.01

(A) Probability to retire before 55 in 2011 (ref: active, aged between 40 and 55)

(B) Probability to move out in 2011 (ref: individuals who will not move out in 2011)

Control variables: sex, age, income, Exp. Phy., SPR1, SPR2


Table 1.6 – Impact of better coverage and chronic disease onset on GP visits and drugs con-sumption (Whole sample)

2SLS Estimations with individual fixed effects, T=2010,2012

Log(GP visits) Log(Drugs)

QUIT -0.04 (0.09) -0.17 (0.16)

Chronic Disease 0.14*** (0.02) 0.62*** (0.03)

* p<0.1, ** p<0.05, *** p<0.01

Other regressors: 2012, income, SPR1, SPR2, Exp. Phy., GP (only for Drugs)


76 Chapter1

Table 1.7 – Instruments: First stage coefficients and F-stat

(1) (2) (3) (4)Whole sample High SPR1 Low & Med SPR1 Low SPR1

First stage coeff / Early retirees 0.37*** (0.02) 0.37*** (0.03) 0.37*** (0.02) 0.39*** (0.03)First stage coeff / Movers 0.11*** (0.01) 0.09*** (0.02) 0.14*** (0.01) 0.13*** (0.02)First stage F-Stat 337.75 92.37 210.14 92.99on excluded instruments

* p<0.1, ** p<0.05, *** p<0.01


Table 1.8 – Robustness check: impact of better coverage when using "early retirees" as theonly excluded instrument


log(Q) log(Q2/Q) log(BB/Q)(2) High SPR1

"Early retirees" only -0.12 (0.28) -0.00 ( 0.09) -0.13 (0.42)"Early retirees" + "movers" -0.05 (0.25) 0.05 (0.08) 0.13 (0.39)

(3) Low & Medium SPR1"Early retirees" only 0.22 (0.17) 0.12** (0.05) 0.41 (0.26)"Early retirees" + "movers" 0.23 (0.14) 0.14*** (0.05) 0.47** (0.22)

(4) Low SPR1"Early retirees" only 0.30 (0.22) 0.12** (0.06) 0.42 (0.26)"Early retirees" + "movers" 0.42** (0.20) 0.14** (0.07) 0.61** (0.31)

* p<0.1, ** p<0.05, *** p<0.01


Appendix 77

Table 1.9 – Robustness check: impact of better coverage on different categories of SPR1 (2SLS)


log(Q) log(Q2/Q) log(BB/Q)(I) High SPR1 (above median) 0.16 (0.23) -0.00 (0.07) -0.05 (0.35)

Low SPR1 (below median) 0.27 (0.17) 0.13** (0.06) 0.51** (0.26)(II) High SPR1 * Medium & High SPR2 -0.01 (0.33) 0.17 (0.11) 0.74 (0.51)

Low & Medium SPR1 * Medium & High SPR2 0.21 (0.15) 0.15*** (0.05) 0.63*** (0.23)

* p<0.1, ** p<0.05, *** p<0.01

Median of SPR1: 45 S1 specialists per 100,000 inhabitants

Medium & High SPR2: above 15 S2 specialists per 100,000 inhabitants


Chapter 2

Selection on moral hazard in

Supplementary Health Insurance

2.1 Introduction

It is critical for insurers to evaluate the possible effect of health insurance on care consumption

when they design their contracts and set their prices. However, when insurance is voluntary, the

estimated relationship between health insurance coverage and healthcare consumption is influ-

enced by endogeneous selection: individual characteristics, such as health status, age, gender,

income, supply side constraints or preferences are likely to explain both individuals’ consump-

tion of healthcare and demand for health insurance. Einav et al. (2013) distinguish two sources

of endogeneous selection: classical adverse selection and selection on moral hazard. Classical

adverse selection is linked to individual heterogeneity as regards demand for healthcare. Basi-

cally, some individuals consume more healthcare than others and are also more likely to buy

insurance in order to reduce the financial risk associated with their healthcare expenditures.

Selection on moral hazard appears when there is individual heterogeneity as regards the be-

havioral response to health insurance. In this case, some individuals might be more prone to

buy insurance because they expect an increase in their healthcare consumption due to better

coverage.

This chapter was jointly written with Brigitte Dormont.

80 Chapter2

Empirical contributions that aim to estimate the causal effect of insurance on healthcare use

acknowledge that there is heterogeneity in the demand for healthcare and control for classical

adverse selection (Cameron et al. 1988, Coulson et al. 1995, Holly et al. 1998, Vera-Hernández

1999, Schellhorn 2001, Buchmueller & Couffinhal 2004, Jones et al. 2006). In this literature,

the response to health insurance is often assumed to be homogeneous across individuals and

moral hazard is estimated through a single parameter associated with the price elasticity of

demand for healthcare. In this framework, results based on randomization such as the RAND

Health Insurance Experiment (Manning et al. 1987, Newhouse 1993), or quasi-natural experi-

ments (Chiappori et al. 1998) are usually considered as a gold standard. Of course, random-

ization is an elegant solution to eliminate selection bias from the estimation of the impact of

insurance on care use. But this approach is not necessarily of interest when insurance is vol-

untary. Because these analyses remove the endogenous choice component from the equation,

they are not able to estimate a potential selection on moral hazard and predict the impact of

a voluntary insurance on healthcare consumption. The question of selection on moral hazard

has been addressed empirically by Einav et al. (2013). They use individual-level panel data

from an American firm where employees can choose among different level of coverage. They

find heterogeneity on moral hazard together with selection on moral hazard: individuals who

buy more comprehensive coverage exhibit greater moral hazard.

Assuming that individuals select themselves in connection with their expected response to insur-

ance can be particularly relevant, especially when one wants to predict the effect of copayments

and deductibles on healthcare expenditures. Suppose that an insurer wants to supply an addi-

tional contract with better coverage. If he relies on average estimates of the price elasticity of

demand1, he will underestimate the increase in costs due to moral hazard. Indeed, contracts

with more comprehensive coverage will attract individuals whose healthcare consumption would

increase more strongly. On the contrary, if the insurer wants to introduce copayments to limit

medical spending, he will overestimate the effect of such a decision: higher copayments will

firstly attract individuals who are less sensitive to healthcare prices. Of course, these concerns

are relevant only if the insurance under review is voluntary and not mandatory. Actually, this

situation deserves attention because it is often encountered: it concerns all the cases where in-

1That would be estimated, for instance, by a random assignment procedure like in the Rand experiment.

2.1 Introduction 81

dividuals can buy supplementary health insurance. However, the empirical literature addresses

issues that are relevant mostly in the case of mandatory health insurance.

In this paper we investigate the relationships between the demand for healthcare, the decision to

take out health insurance and the behavioral response to better coverage with a structural model

that specifies individual heterogeneity in demand for healthcare and response to insurance (i.e.

moral hazard). We set the analysis in the French context where individuals can voluntarily take

out supplementary health insurance (SHI) which covers medical goods and services with higher

quality than the basic healthcare basket covered by mandatory national health insurance (NHI).

We especially focus on the demand for specialist who balance bill their patients, i.e. charge

them more than the regulated fee set by NHI. We estimate the causal effect of voluntary SHI on

the demand of specialist consultations with balance billing, taking into account both classical

adverse selection and selection on moral hazard. The econometric analysis is performed on a

French database of 58,519 individuals observed in 2012.

In France, the NHI offers universal, yet partial, coverage. Individuals can take out SHI to

enhance their coverage and limit out-of-pocket expenditures, either voluntary in the individual

market or through their employer. For ambulatory care, the NHI sets a regulated price and

reimburses only a fraction of it to patients (70% of the regulated fee for specialist consultations).

On top of NHI copayments, patients may also have to pay balance billing. Indeed, patients have

the choice to visit two types of specialists: ‘sector 1’ (S1) specialists are mandated to charge

the NHI regulated fee whereas ‘sector 2’ (S2) specialists are allowed to balance bill, i.e. charge

a fee that exceeds the regulated price, which is the basis for NHI reimbursement. S1 and S2

specialists are supposed to provide the same medical service. However, because S2 is restricted

to physicians who have been practicing in a qualifying hospital setting, S2 consultations can be

associated by patients with a higher level of quality. Because they charge higher fees, waiting

lists are also likely to be shorter for S2 specialists. Almost 95% of the French population is

covered by a SHI contract, which covers at least the 30% NHI copayment. Still, there are

important differences between SHI contracts in terms of balance billing coverage: in polls, only

48.5% of SHI policyholders state that they are well covered against balance billing (Célant et al.

2014).

82 Chapter2

In the specific context of demand for balance billing coverage we can expect both forms of

selection, e.g. classical adverse selection and selection on moral hazard. Indeed, in Dormont &

Péron (2016) we gave evidence of individual heterogeneity in balance billing consumption re-

lated to demand for more comprehensive SHI coverage. Our estimates were based on a French

panel data set of 43,111 individuals observed in 2010 and 2012. In 2010, the whole sample was

covered by the same SHI contract, with no coverage against balance billing. We were able to

observe the same individuals in 2012 after 3,819 of them had switched to other SHI contracts

that cover balance billing. Using individual fixed effects and instrument variables we were able

to deal with the non-exogeneity of the decision to switch insurer and estimate the change in

balance billing consumption between 2010 and 2012 due to a better coverage. Our estimates

show that those who ask for better coverage consume, ceteris paribus, more balance billing

than the rest of the sample, even when they are not covered for balance billing. This would

reveal classical adverse selection in the demand for balance billing coverage. Heterogeneity in

the response to better coverage can be linked to unobservable individual heterogeneity, and to

observable characteristics. First, the response to a better balance billing coverage is likely to

be influenced by unobservable individual characteristics. Indeed, the demand for S2 visits relies

strongly on perceived quality of care. Preferences and beliefs, which are unobserved, are likely

to be heterogeneous: they can explain both heterogeneous response to a better coverage and

decision to take out SHI resulting in selection on moral hazard. Second, heterogeneity in moral

hazard might as well be influenced by observable characteristics such as gender, age, income or

living area. In Dormont & Péron (2016) we found evidence of moral hazard only for individuals

living in areas where there are few specialists who do not balance bill their patients (S1 spe-

cialists)2. Turning to a possible impact of income, we can refer to Nyman’s contribution to the

debate on moral hazard (Nyman 1999, 2003). Traditional models of health insurance (Friedman

& Savage 1948, Pauly 1968) see moral hazard as a pure price effect: because better insurance

coverage reduces the price faced by patients and assuming the negative price-elasticity of health-

care demand, patients with insurance coverage should increase their healthcare consumption.

However, Nyman considers that better coverage also creates an income effect which releases the

budget constraint and gives patients access to care that they could not afford without insur-

2This is because the effect of insurance on the relative price of S1 and S2 consultations depends on the searchand waiting time costs associated with a S1 consultation, which are strongly influenced by S1 availability in eacharea

2.1 Introduction 83

ance. Within this framework, low income individuals should react more to an improvement in

coverage than rich individuals.

In the econometric literature, selection on moral hazard is more generally known as selection on

returns or essential heterogeneity. Assuming that there is individual heterogeneity in treatment

effects, essential heterogeneity arises when individuals decide to take the treatment in relation

with their expected response to the treatment. Heckman & Vytlacil (2007) show that in the

presence of essential heterogeneity, instrumental variable (IV) methods, which are frequently

used to control for endogeneous selection, do not estimate an average treatment effect (ATE),

nor a treatment effect on treated. Indeed, IV methods only estimate a local average treatment

effect (LATE), specific to individuals who would react to the shock induced by the instrument.

In the presence of essential heterogeneity, this local effect cannot be extended to the average

population. Another consequence is that different instruments are likely to give different es-

timates of the treatment effect because they rely on compliers with different reactions to the

treatment. Beyond the objective to estimate unbiased causal effects, we can question the rele-

vance of estimating an ATE in a context where individuals can decide to participate or not in

the treatment. Indeed, in this case, we pay more attention to the treatment effect of those who

are more likely to take the treatment rather than to the average effect on the whole population.

Marginal treatment effects (MTE) estimators have been developed to capture the impact of

a treatment likely to vary within a population in correlation with observed and unobserved

characteristics, in a setting where individuals select themselves into treatment. First defined

by Bjorklund & Moffitt (1987), MTE have been comprehensively described by Heckman & Vyt-

lacil (2001) and Heckman et al. (2006). Empirically, MTE have been used to capture returns in

education (Carneiro et al. 2011), breast cancer treatment effects (Basu et al. 2007) or the effect

of family size on children’s outcome (Brinch et al. 2012). Recently, Kowalski (2015) uses MTE

in an experimental framework to assess the external validity of the Oregon health insurance

experiment.

MTE are the appropriate tools when one focuses on the effect of voluntary health insurance

on balance billing consumption. First, essential heterogeneity is only a concern if individuals

can decide to take the treatment and if unobservable characteristics can influence their out-

come. In our setting, individuals can choose their level of balance billing coverage while their

84 Chapter2

preferences for higher quality of care, which are unobservable to the econometrician, are likely

to influence their balance billing consumption. Second, MTE rely on a structural approach

that links the output (the demand for balance billing), the decision to take the treatment (take

out SHI) and the treatment effect (moral hazard). This unified framework identifies complex

relationships between demand for higher quality of care and comprehensive SHI. It allows to

identify different motives of the demand for balance billing coverage, either to cover expected

expenditures or to increase balance billing consumption. Third, MTE fully take into account

individual heterogeneity in the response to treatment, due to both observable and unobservable

characteristics. The structural approach further associates the heterogeneous treatment effect

to different mechanisms related to income, supply side constraints or preferences. We are indeed

able to give some ‘content’ to moral hazard, especially in terms of access to S2 specialists, and

go beyond the homogeneous price effect usually reported in the literature.

In this paper, we estimate the marginal treatment effect of SHI coverage on balance billing

consumption. We take into account observed and unobserved individual heterogeneity in the

demand for S2 consultations and in moral hazard. We also control for classical adverse selection

and selection on moral hazard. Our empirical analysis is built on a structural model that links

(i) the demand for balance billing, (ii) the decision to take out more comprehensive SHI and

(iii) the behavioral response to better coverage. Thanks to this unified framework we are able

to give insights on the determinants of the demand for higher quality of care and the role of

health insurance in terms of access to care, especially for low income individuals.

Our database stems from administrative data provided by a French insurer, the Mutuelle

Générale de l’Education Nationale (MGEN). We use cross-sectional data which provide for

58,519 individuals information on healthcare claims and reimbursements by the NHI and SHI

in 2012. We are able to observe two groups of individuals: MGEN-SHI subscribers and better-

SHI subscribers. The former are not covered for balance billing. The latter were previously

covered by the same MGEN-SHI contract but decided in 2011 to switch towards another SHI

insurer: in 2012 they benefit from balance billing coverage. The better-SHI subscribers are used

as a treatment group to estimate the heterogeneous effect of SHI coverage on balance billing

consumption and test for the existence of classical adverse selection and selection on moral

hazard.

2.2 Method: Marginal Treatment Effects 85



take out better SHI are also those who exhibit stronger moral hazard, i.e. a larger increase

in balance billing per consultation. We also find that individuals’ income is a strong determi-

nant of balance billing consumption and influence the behavioral response to better coverage.

Without coverage, the poor consume less balance billing than the rich but increase their con-

sumption more sharply once covered for balance billing. They are also more likely to subscribe

to comprehensive coverage.

The fact that unobservable characteristics influence both the decision to take out SHI and the

magnitude of moral hazard is firstly a concern for insurers. Indeed, when providing compre-

hensive balance billing coverage, insurers have to take into account that their contract is likely

to attract individuals who are more sensitive to healthcare prices and respond more sharply

than average to better coverage. In a context where SHI is voluntary, the inflationary impact

of SHI coverage might be worsened by selection on moral hazard. Our policy conclusions as

regards the role of income are of different nature. We argue that the negative effect of income

on the demand for S2 consultations coupled with its positive effect on moral hazard reveals that

insurance plays an important role in terms of access to care.

This paper is organized as follows. Section 2.2 presents the MTE method. In section 2.3 we

present our data and empirical strategy. The empirical specification is developed in section 2.4.

Results are presented in section 2.5. Section 2.6 concludes.

2.2 Method: Marginal Treatment Effects

Allowing for heterogeneity in treatment effects potentially yields essential heterogeneity. This

term means that the assignment to treatment, or the choice to be treated, is correlated with

the treatment impact. In our case, some people would choose to take out better supplementary

insurance because they know their healthcare consumption will respond positively to better cov-

erage. As stated by Heckman et al. (2006), when treatment effects are likely to be heterogenous,

it is reasonable to allow for a correlation between the choice for treatment and the treatment

impact.

86 Chapter2

Consider the two potential outcomes Yi,1 = α1 + Ui,1 and Yi,0 = α0 + Ui,0 which are observed if

the individual is respectively treated (Di = 1) or not treated (Di = 0). The observed outcome

is:

Yi = DiYi,1 + (1 − Di)Yi,0

= α0 + ((α1 − α0) + (Ui,1 − Ui,0))Di + Ui,0

Here the treatment impact varies across individuals. One has: Yi = α0 + τiDi + Ui,0 with

τi = Yi,1 − Yi,0 = (α1 − α0) + (Ui,1 − Ui,0).

To estimate this model one has to deal with two possible selection problems: (i) a correlation

between Di and Ui,0, which is due to a selection on the level of the outcome without treatment;

(ii) a correlation between Di and τi, i.e. a selection on the expected impact of the treatment

(essential heterogeneity). In case of essential heterogeneity, the use of instrumental variables

is not straightforward. Firstly, the IV method does not provide a consistent estimation of the

mean treatment effect τ . 3 Secondly, if there is selection on the gains from treatment, the IV

estimate must be interpreted as a local average treatment effect "which is only informative about

the average causal effect of an instrument-induced shift in D" (Brinch et al. 2012). As shown

by Heckman et al. (2006), the solution is to estimate marginal treatment effects (MTE). MTE

are computed from a model that explicitly specifies the decision to be treated, and gives the

treatment impact for someone who is at the margin, i.e. who is indifferent between being treated

or not. Moreover, MTE produce a function that is invariant to the choice of instruments.

3One has: τi = (α1 − α0) + (Ui,1 − Ui,0) = τ + ηi

From Yi = α0 + τiDi + Ui,0, one has: Yi = α0 + τDi + (Ui,0 + ηiDi)To provide a consistent estimate of τ , the IV Z must be uncorrelated with Ui,0 + ηiDi. In the case of essential

heterogeneity this condition is not satisfied, even if Z is not correlated with Ui,0 and ηi . Indeed, E(ηiDi|Zi ) =E(ηi|Di = 1,Zi ) Pr(Di = 1|Zi ), and the first term of the right-hand side is different from 0 if the decision totreat is correlated with the individual gain of the treatment.


2.2.1 The Generalized Roy model

To introduce MTE, Heckman et al. (2006) consider the Generalized Roy model, which is a

switching regression model that allows a structural approach to policy evaluation.4 For the

sake of simplicity, the subscripts i are omitted hereafter. The model specifies the two potential

outcomes (Y0, Y1) and the decision to participate in the treatment (D = (0,1)). The choice of

receiving treatment is modeled as a function of observables Z and unobservables V , and linked

to the observed outcome Y through a latent variable D∗. In addition to the previous model, we

now assume that the outcomes depend on exogenous regressors X. Hence, the treatment has

an impact on unobserved heterogeneity (from U0 to U1) and on the effect of covariates X (from

β0 to β1):

Y = DY1 + (1 − D)Y0 (2.1)

Y1 = α1 + Xβ1 + U1 (2.2)

Y0 = α0 + Xβ0 + U0 (2.3)

D∗ = Zγ − V (2.4)

D =

1 if D∗ > 0

0 if D∗ ≤ 0(2.5)

We assume that U0, U1 and V are independent of Z, conditional on X. In addition, the

probability of treatment is a non-trivial function of Z, conditional on X : Pr(D|X = x,Z =

z) 6= Pr(D|X = x) (Basu et al. 2007).

The propensity score P (Z) is the probability of receiving treatment conditional on Z:

P (Z) ≡ Pr(D = 1|Z = z) = Pr(V < Zγ|Z = z) = FV (Zγ)

where FV is the cumulative distribution function of V , hence a monotonic and absolutely con-

tinuous function.

4Our description of the statistical framework follows closely that found in Heckman et al. (2006) and Braveet al. (2014).

88 Chapter2

An individual chooses to be treated if the latent variable D∗ is positive:

D = 1 ⇔ D∗ > 0 ⇔ Zγ > V ⇔ FV (Zγ) > FV (V ) ⇔ P (Z) > FV (V )

Defining UD = FV (V ), the condition to be treated is that the propensity score is greater than

UD : P (Z) > UD.

Without a loss of generality we can assume that UD is a uniformly distributed random variable

between 0 and 1. In this case the pth quantile of UD is p and different values of UD correspond

to different quantiles of V.

The propensity score must be interpreted as the incentive to choose the treatment, for given

covariates Z. As for UD, it can be seen as the individual idiosyncratic disutility of taking

the treatment. Conditionally on her characteristics z, which provide a propensity score p,

an individual will ultimately take the treatment if her disutility uD is lower than p (and be

indifferent if uD = p). For the econometrician, variables Z are observable and realizations uD

are not observed. Given that values of UD are quantiles of V, it is possible to compare P (Z)

and UD on the same interval [0,1] on the horizontal axis (Figure 2.1):

2.2.2 Marginal Treatment Effects

In our framework, decision to participate in the treatment and treatment impact vary across

individuals. MTE capture the treatment effect (Y1 − Y0) for the ‘marginal individual’ who is

indifferent between being treated or not, conditional on her observable characteristics X = x.

By definition, the marginal individual has a propensity score equal to her disutility of taking

the treatment: UD = p.

MTE ≡ E(Y1 − Y0|X = x, UD = p) (2.6)

Heckman et al. (2006) show how MTE can be identified by taking the derivative of E(Y |X =

x,Z = z) with respect to P (Z). First, note that


E(Y |X = x,Z = z) = E{Y |X = x,P (Z) = p} (2.7)

Following Heckman & Vytlacil (2001), the observed outcome can be written as:

E{Y |X = x,P (Z) = p} = E(Y0|X = x) + E(Y1 − Y0|X = x, D = 1)p (2.8)

= E(Y0|X = x) +∫ p

0E(Y1 − Y0|X = x, UD = uD)duD (2.9)

As a consequence,

∂E{Y |X = x,P (Z) = p}

∂p= E(Y1 − Y0|X = x, UD = p) (2.10)

Expression (2.10) shows how the derivative of E(Y |X = x,Z = z) identifies marginal treatment

effect, i.e the expected treatment effect conditional on X and UD5. As noted by Heckman

et al. (2006), "a high value of P (Z) = p identifies MTE at a value of UD = uD that is high -

that is associated with nonparticipation". Indeed, that individuals with a high propensity score

are indifferent between being treated or not implies that they have a very high idiosyncratic

disutility of taking the treatment uD. Therefore, MTE with high p values identify returns for

individuals who are less likely to take the treatment. Conversely, MTE with low values of p

identify returns for individuals prone to take the treatment.

2.2.3 Estimation

Combining (2.8) with the expressions of Y1 and Y0 in (2.2)-(2.3), one obtains:

E{Y |X = x,P (Z) = p} = α0 + xβ0 + (α1 − α0)p + {x(β1 − β0)}p + K(p) , (2.11)

with K(p) = E{U0|P (Z) = p} + E{U1 − U0|P (Z) = p}p (2.12)5The ATE, by contrast, is the average treatment effect, conditional on X. Note that the ATE can be

constructed as a weighted average of MTE by integrating over UD (Heckman & Vytlacil 2001, Heckman et al.2006), providing that the support of UD covers [0,1]: AT E ≡ E(Y1 − Y0|X = x).

90 Chapter2

K(p) serves here as a control function, as defined by Heckman & Robb (1985). It takes into

account the fact that the difference between the outcome and the specification on the right-hand

side is a function of p. Hence, a regression applied on (2.11) consistently estimates parameters

(α0,α1,β0,β1).

As stated above, the MTE are computed as the partial derivative of the conditional expectation

of Y with respect to P (Z) :

∂E{Y |X = x,P (Z) = p}

∂p= (α1 − α0) + x(β1 − β0) +

∂K(p)∂p

(2.13)

The first step consists in estimating the propensity score for each individual, P (z) = Pr(Zγ >

V |Z = z) = p. The propensity score can be fitted by a probit or logit model6.

Writting K(p) as a polynomial in p , equation (2.11) becomes:

E{Y |X = x,P (Z) = p} = α0 + xβ0 + (α1 − α0)p + {x(β1 − β0)}p +ϑ∑

i=1

φipi (2.14)

A parametric estimation of the MTE can be obtained from:

MTE{X = x,P (Z) = p} = (α1 − α0) + x(β1 − β0) +ϑ∑

i=1

iφipi−1, (2.15)

using the estimations of α1 − α0, β1 − β0 and φi obtained from the linear regression implied

by (2.14).

Alternatively we can adopt a semi-parametric approach by running a local polynomial regres-

sion (Fan & Gijbels 1996) on

y = y − α0 − xβ0 + (α1 − α0)p − {x(β1 − β0)}p.

The semi-parametric estimator can only be estimated on the common support of the propensity

score. Precisely, the common support assumption requires that there exist positive frequencies

6It is preferable not to consider a linear probability model because it does not allows to constrain the rangeof P (z) to be (0,1), see Brave et al. (2014).


of P (z) for individuals that receive (D = 1) and do not receive (D = 0) the treatment. It is

worth noting that, although a parametric estimator of MTE can be estimated on the whole

range [0,1], its precision also crucially depends on the common support (Brave et al. 2014).

Therefore, our interpretation of the results will be limited to the common support7.

2.3 Data and empirical strategy

We use a data set from a French supplementary insurer: Mutuelle Générale de l’Education

Nationale (MGEN), which is a not-for-profit insurer who provides mandatory basic health in-

surance for teachers and Ministry of education’s employees. MGEN also supplies supplementary

health insurance in the form of a unique8 contract (MGEN-SHI) which offers a minimal supple-

mentary coverage: it covers only copayments and not balance billing. People can subscribe to

this MGEN-SHI on a voluntary basis, or take out another SHI. For historical reasons, MGEN

manages both basic (NHI) and supplementary insurance (MGEN-SHI). Our data stemmed from

administrative MGEN data: they provide, for each policyholder, detailed information about her

medical bills and reimbursements for basic health insurance and for supplementary insurance

when the individual is a MGEN-SHI subscriber.

In France, ambulatory care is mostly provided by self-employed physicians paid on a fee-for-

service basis. Since 1980, physicians can choose between two contractual arrangements with the

regulator. If they join "Sector 1", physicians are not permitted to balance bill. They agree to

charge their patients the reference fee (23e in 2012 for a routine visit), and get fiscal deductions

in return. If they join "Sector 2", they are allowed to set their own fees. Access to Sector 2

being strongly limited for GPs since 1990, most of them belong to Sector 1: they are 87% in

2012. Hence the issue of balance billing concerns mostly specialists. Balance billing adds 35%

to the annual earnings of Sector 2 specialists. The average proportion of specialists operating

in Sector 2 amounts to 42% in 2012. This proportion varies dramatically across specialties: for

7We do not consider other methods that are available to estimate MTE. Heckman et al. (2006) estimate (2.13)using the Local Instrumental Variable (LIV) approach. However, Brinch et al. (2012) show that LIV does notidentify MTE when the excluded instrument is binary. They develop a method to identify MTE in a fullynon-parametric approach using a binary instrument and a single binary covariate.

8This is true for our observational period. From 2016 on, MGEN started to supply a choice between differentcontracts for SHI.

92 Chapter2

instance, the proportion of specialists operating in Sector 2 is 19% for cardiologists, 73% for

surgeons and 53% for ophthalmologists.

Actually, we do not observe the coverage of balance billing for people who subscribed to another

SHI than MGEN-SHI. However, MGEN used to send a questionnaire to people who switched to

another SHI. This allows us to know, for people who have terminated a MGEN-SHI contract,

if they have subscribed to another SHI. For this reason, we selected, for year 2012, a sample of

subscribers of MGEN-SHI and of subscribers of another SHI, who were in 2010 subscribers of

MGEN-SHI and have terminated their contract in 2011. In this case, we know that their new

coverage will be at least equal and probably better than before, because MGEN-SHI coverage

on balance billing is zero. We name this new contract ‘better-SHI’.

Because in France balance billing concerns mostly specialists, our analysis focuses on the impact

of coverage of balance billing on the use of specialists. We leave the differences in differences

approach used in Dormont & Péron (2016) to specify, on a cross section of individuals observed

in 2012, a Roy model for the issue at stake. It is a switching regression model that explains

together the decision to take out coverage for balance billing (better-SHI), and the demand for

consultations with balance billing when the individual is – or is not – covered for balance billing.

As stated above, such a specification enables us to estimate the impact of better coverage on the

use of balance billing in case of essential heterogeneity. For that purpose, we use an instrument

which explains the decision to take out better coverage and which is not directly related to

balance billing consumption.

Our original sample was composed of 91,629 subscribers of MGEN-SHI and 8,249 subscribers

of better-SHI. We excluded individuals who live outside continental France as well as the top

1% of care users in 2012. Because we focus on specialist consultations, we only keep individuals

who have at least one visit to a specialist in 2012, with or without balance billing. Our final

sample includes 58,519 individuals: 53,456 subscribers of MGEN-SHI and 5,063 subscribers of

better-SHI, observed in 2012, who have visited a specialist at least once in 2012.

Our empirical strategy requires the use of an instrument to explain the decision to terminate

MGEN-SHI contract in order to take out a better-SHI. A valid instrument must be correlated


to the decision to quit MGEN-SHI and, conditional on other observable characteristics, be

uncorrelated to the consumption of balance billing (in the Roy model, we assume that U0, U1

and V are independent of Z, conditional on X). The decision to retire in 2011 for people

younger than 55 years-old, that we used in Dormont & Péron (2016), is a reliable instrument.

The age threshold refers to a specific right for teachers and civil-servant who raised three or

more children to retire before 55. This right has been revoked in January 2012, creating an

important incentive for individuals meeting the criteria to retire in 2011. Indeed, MGEN-SHI

premiums raise from 2.97% of wages before retirement to 3.56% of pensions after. We argue that

this retirement policy change creates an exogeneous shock that gives individuals incentives to

terminate their MGEN-SHI contract for a better-SHI, but has no reason to drive their balance

billing consumption. In our sample, 368 individuals decided to retire in 2011 and half of them

quit MGEN-SHI the same year. When including retirement before 55 as a covariate in a simple

log-linear model that explains balance billing consumption, the coefficient is non significantly

different from zero. Therefore, we decide to rely on the ‘early retirees’ instrument to explain

the decision to subscribe to better-SHI9.

Our data provide, for each individual in 2012 the number of visits to a specialist Q, including

the number of visits to S2 specialists who charge balance billing, Q2, as well as the total

amount of balance billing, BB. We focus on four variables of interest: the number of specialist

consultations, Q (with Q ≥ 1), the proportion of S2 consultations, Q2/Q, the average balance

billing per consultation, BB/Q and the average balance billing per S2 consultation BB/Q2

(computed only for individuals who have at least one S2 consultation in 2012). We are able to

distinguish three dimensions in the demand for specialist consultations: quantity of specialist

consultations, quality in terms of choice between S1 and S2 specialists and finally the average

price per consultation to a S2 specialist, which might be linked to quality.

Given that our data do not provide the fee for each consultation, we compute for each indi-

9Note that the condition of independence between the instrument and balance billing consumption is moredemanding with cross-sectional data than it was with panel data in Dormont & Péron (2016), where the specifi-cation of individual fixed effects makes it possible to deal with time-invariant sources of non exogeneity. In thisframework, the need of excluded instruments was only dictated by possible unobservable health or informationshocks that would have explained both the switch of SHI and a ‘change’ in balance billing consumption. Herewe need an instrument that is not correlated with the ‘level’ of balance billing consumption. As explained above,this condition is fulfilled for ‘retirement before the age of 55’. But it is not the case for the fact of ‘moving outto another département’. We cannot use this variable as an instrument for our cross-section analysis.

94 Chapter2

vidual an annual average of balance billing per consultation. However, we are able to control

for the individual’s needs regarding medical specialties. This is important because, as shown

in Dormont & Péron (2016), the availability of S1 and S2 specialists varies dramatically from

a specialty to another in France. Gynecologists, ophthalmologists, surgeons and ENT special-

ists10 charge balance billing in a larger proportion than their colleagues. As a matter of fact,

patients’ choice to visit a S2 is likely to be far more constrained when they need to visit one of

these specialties. We therefore use a dummy variable called ‘expensive physicians’ (ExpPhy)

which equals 1 when the individual visited one of these specialists at least once in 2012.

Our information on individual characteristics include gender, age, income and health status. To

make the interpretation of the results easier, we build three age groups, 20-40, 40-60 and over

60 years old. Our income variable is based on individuals’ wage or pension used by MGEN to

compute MGEN-SHI premiums. The dummy CD, which equals 1 if individuals have a chronic

disease, is used as an indicator of health status. Access to S1 or S2 specialists is not only a

question of price (balance billing or not), but also a question of geographical access (transporta-

tion costs) or waiting time. To measure the respective availability of S1 or S2 specialists, we use

the ‘specialist : population ratios’ (SPR) provided by national statistics in 2012. The SPR is

the number of specialists either in S1 (SPR1) or in S2 (SPR2) per 100,000 inhabitants in each

département.

2.3.1 Basic features of the data

Table 2.1 displays the characteristics of the 58,519 individuals of our final sample: there is a high

proportion of women (72.5%), the average age is close to 58 years, the average income amounts

to e2,500 and 22% have a chronic disease. In comparison, the average wage is in France equal

to e2,15711 and 19.5%12 of people have a chronic disease. These characteristics derive from the

fact that (i) MGEN covers teachers and civil servant who have a certain education level and

are mostly women; (ii) we have restricted our sample to those who visited a specialist at least

once in 2012.

10Ear, Nose and Throat specialists11Average net mensual wage in 2012; source: INSEE12source: ESPS survey


Compared to MGEN-SHI holders, better-SHI holders are on average 12 years younger, count

more women (82% vs 72.5%) and less individuals with chronic disease (9.4% vs 22%). To sum up,

those who decided to quit MGEN-SHI are on average younger and healthier. This is a common

result in the literature on switching behavior: in the USA (Buchmueller & Feldstein 1997,

Strombom et al. 2002), Switzerland (Dormont et al. 2009) or in the Netherlands (Duijmelinck

& van de Ven 2016), switchers are invariably younger and also tend to be healthier. We discuss

the motivations to subscribe to better-SHI further in the paper.

Table 2.2 displays statistics about the use of specialist visits and balance billing in 2010 and

2012 for MGEN-SHI holders and future better-SHI holders (who are covered by MGEN-SHI

in 2010 and better-SHI in 2012)13. Of course, in 2012, better-SHI holders are likely to have

a better coverage for balance billing than MGEN-SHI holders. Whereas the total number of

visits (Q) is not significantly different between MGEN-SHI and better-SHI holders, the latter

consume significantly more balance billing, both in quantity (Q2 = 1.7 for better-SHI holders

vs 1.3 for MGEN-SHI holders) and price (BB/Q2 = 26.1 vs 24.2). Consequently, better-SHI

holders’ mean consumption of balance billing, (BB), amounts to e46.9 in 2012, which is 42.6%

higher than for MGEN-SHI holders.

These differences might reflect adverse selection, as well as moral hazard and, if there is hetero-

geneity in moral hazard, possible selection on moral hazard. Actually, our data design enables

us to observe the use of balance billing by better-SHI subscribers in 2010, before they take

out better coverage. In 2010, all individuals in our sample, including future better-SHI, are all

MGEN-SHI holders, hence not covered for balance billing. Table 2.2 shows that in 2010 the fu-

ture better-SHI holders, who will quit MGEN-SHI the next year, consumed more balance billing

than those meant to stay under MGEN-SHI contract. This reveals classical adverse selection:

those who ask for better coverage consume more balance billing than others.

13This comparison is not possible for all the 58,519 individuals observed in 2012 since only 43,612 of themused at least a specialist visit in 2010.

96 Chapter2

2.4 Empirical specification

The aim of this paper is to estimate the effect of health insurance on the consumption of

balance billing when moral hazard is heterogeneous. Assuming that moral hazard may be

related to the decision to choose a better coverage for balance billing, we estimate MTE to

capture heterogeneity in response to health insurance and to test for essential heterogeneity.

Also, our estimation strategy enables us to evaluate the effect of observable characteristics, such

as income, on the consumption of balance billing, on the demand for better SHI coverage and

on moral hazard.

2.4.1 Model and estimation

Following the generalized Roy model presented in section 2.1, we specify a choice equation

explaining the individual’s decision to take out another SHI to enjoy better coverage (better-

SHI) than the one provided by MGEN-SHI. The estimation of this choice equation enables us

to understand coverage choices’ determinants and provides the propensity scores that are used

to identify MTE.

The choice is specified through the binary variable D, which is equal to 1 if the individual

chooses to take out better-SHI in 2011. In 2012, people covered by better-SHI benefit from

balance billing coverage whilst MGEN-SHI enrollees (those who stayed) do not. The decision

depends on the sign of a continuous latent variable D∗:

D∗ = xγ1 + γ2EarlyRetiree − V = Zγ − V (2.16)

D =

1 if D∗ > 0

0 if D∗ ≤ 0(2.17)

EarlyRetiree is our excluded instrument: the decision to retire before 55 years old is correlated

with the decision to subscribe to better-SHI, but not with the consumption of balance billing.

x is a vector of covariates which includes individuals’ gender, age, income and whether they

suffer from a chronic disease. It includes also local availability of specialists of sector 1 (S1,

2.4 Empirical specification 97

not allowed to charge balance billing) and 2 (S2, allowed to charge balance billing) and for the

individual’s needs as regards medical specialty (the proportion of S2 specialists is particularly

high for ophthalmologists, gynaecologists and ENT). V is an unobservable random variable

corresponding to the individual idiosyncratic disutility of choosing better-SHI (linked with un-

observable individual characteristics such as disutility of administrative switching costs, belief

that sector 2 doctors provide better quality of care, and risk aversion, i.e. utility of coverage

for given risk level).

P (Z) is the propensity score, i.e. the probability of choosing better-SHI conditional on Z. As

explained in section 2, it is useful to define UD = FV (V ), where FV is the cumulative function of

V. UD is a random variable uniformly distributed between 0 and 1 and values of UD correspond

to quantiles of V . For a given level of Z, individuals who have a large UD are less likely to take

out better-SHI.

D = 1 ⇔ Zγ > V ⇔ FV (Zγ) > FV (V ) ⇔ P (Z) > UD

We rely on the parametric and semi-parametric approaches presented in section 2.3 to estimate

MTE. We estimate the propensity score P (z) = p for each individual with a Probit model14.

We then determine the common support, i.e. the values of P (z) = p for which we have positive

frequencies of individuals who decided to take out better-SHI (D = 1) and of individuals who

remained MGEN-SHI enrollees (D = 0).

Then we perform OLS on equation (2.14), assuming that the function K(p) is a polynomial of

degree 3:

y = α0 + xβ0 + (α1 − α0)p + {x(β1 − β0)}p + φ1p + φ2p2 + φ3p3 (2.18)

y is the log-transformation of one of our four variable of interest: Q the number of specialists con-

sultations, Q2/Q the proportion of S2 consultations in the total of visits to a specialist, BB/Q

the average amount of balance billing per visit, BB/Q2 the average amount of balance billing

14The results are robust to the use of a Logit model.

98 Chapter2

per S2 visit. As for the choice equation, x is a vector of covariates which includes individuals’

gender, age, income, chronic disease, local availability of S1 and S2 specialists, and individual’s

needs regarding ophthalmologists, gynaecologists and ENT. Subscript 1 (respectively, 0) refers

to better-SHI enrollees (respectively, to MGEN -SHI enrollees). Better-SHI enrollees benefit

from balance billing coverage, but this is not the case for MGEN-SHI enrollees. According to

the Roy model, when an individual chooses to switch from MGEN-SHI to better-SHI, his or

her behavior switches from Y0 = α0 + Xβ0 + U0 to Y1 = α1 + Xβ1 + U1.

The parametric estimator of MTE is computed for given values x as

MTE{x,p} = (α1 − α0) + x(β1 − β0) + φ1 + φ2p + φ3p2 (2.19)

In our setting, MTE capture the effect of having better balance billing coverage for the individual

‘at the margin’, who is indifferent between subscribing to better-SHI or remaining enrolled in

MGEN-SHI (UD = p).

We also compute a semi-parametric estimator of MTE by running a local polynomial regression

of y on p with:

y = y − α0 − xβ0 + (α1 − α0)p − {x(β1 − β0)}p. (2.20)

Note that the semi-parametric approach differs only in the estimation of the unobservable

component K(p).

To run the estimations, we use the Stata command margte (Brave et al. 2014) with a polynomial

of degree 3 to estimate the parameters of the MTE. We use an epanechikov kernel function in the

nonparametric estimation. Standard errors are computed using bootstrap (50 reps). Parametric

and semi-parametric MTE are computed at mean values of x as in equations (2.21) and (2.22):

MTE{x,p} = (α1 − α0) + x(β1 − β0) + φ1 + φ2p + φ3p2 (2.21)

MTE{x,p} = (α1 − α0) + x(β1 − β0) +∂K(p)

∂p(2.22)

2.4 Empirical specification 99

2.4.2 Interpretation of the estimates

Our empirical specification allows for a detailed analysis as regards the impacts of observable

characteristics:

• β0 captures the impacts of individual characteristics on the demand for S2 consultations

without balance billing coverage;

• γ captures their effect in the decision to switch;

• In addition, we estimate the change (β1 − β0) in the impact of regressors which is due to

better coverage.

Note that in our model the fact that the impacts of regressors can be modified by better coverage

is a source of heterogeneity in moral hazard that comes in addition to the heterogeneity linked

to unobserved characteristics. Suppose that (β1 − β0) < 0 for income. This would mean that

low-income people react more strongly to insurance.

In what follows, we first examine the estimates obtained for β0, γ and (β1−β0). Then we compare

their signs to identify the situations of classical adverse selection (relationship between β0 and

γ) and the situations of selection on moral hazard (relationship between (β1 − β0) and γ).

As regards essential heterogeneity, Heckman et al. (2006) propose a simple test to explore

the assumption of a variable treatment effect due to unobservable characteristics. The joint

significance of the polynomial coefficients φ1,φ2,φ3 in equation (3.4) reveals the presence of

essential heterogeneity. Indeed, the signs of φ2 and φ3 determine the slope of the curve that

characterizes the relationship between the treatment effect and the value of UD. Precisely,

φ1 = φ2 = φ3 = 0 would mean that the treatment effect does not vary with unobservable

characteristics, i.e. there is no evidence of essential heterogeneity. On the contrary, depending

on the values of φ2 and φ3 , one can find that individuals with a low (or high) disutility to

switch benefit more (or less) from better balance billing coverage.

Because the common support is not defined for all values of UD between 0 and 1, we are not

able to compute an ATE with the semi-parametric approach. Note that although parametric

100 Chapter2

MTE are estimated on [0,1], their precision strongly decreases for UD > 0.35 which makes the

value of MTE difficult to interpret for higher values of UD. So, in any case, we restrict our

analysis of MTE on the values corresponding to the common support.

2.5 Results

Results are presented in Tables 2.3 to 2.7. Table 2.3 displays the effects of observable individual

characteristics on the demand for better-SHI. Table 2.4 displays the effect of observable char-

acteristics on consumption for balance billing without coverage and on moral hazard. Table 2.5

summarizes the influence of observable characteristics and gives evidence of adverse selection

and selection on moral hazard. Tables 2.6 and 2.7 show evidence of heterogeneity on moral

hazard. Figures 2.3 and 2.4 display respectively parametric and semi-parametric MTE over UD

evaluated at mean values of x with 95% confidence intervals computed from a non-parametric

bootstrap.

2.5.1 Influence of observable characteristics: consumption of balance billing

without coverage

The determinants of the amount of balance billing paid by patient who do not benefit from

insurance coverage are captured by the coefficients β0 (Table 2.4). Income, medical needs and

availability of S1 and S2 specialists appear as the main determinants. The average amount of

balance billing per consultation significantly increases with income: a 10% increase in income

drives up BB/Q by 5.3%. Individuals aged of 60 years old and more, those who suffer from a

chronic disease or visit gynaecologists, ophthalmologists or ENT specialists consume also more

balance billing than others. The availability of S1 and S2 specialists has also a very strong

impact on the amount of balance billing paid by patients. BB/Q is 18% higher for patients

living in départements where the number of S1 specialists is low and 56% higher for those who

lived in départements where S2 specialists are numerous.15

15For the sake of interpretation, we use three categories for SPR1: low SPR1 includes the first third ofdépartements in terms of SPR1 (SP R1 ∈ [20,41[), medium SPR1 the second third (SP R1 ∈ [41,52[), high SPR1the last third (SP R1 ∈ [52,56]). We proceed with the same method for SPR2 but only present two categories:low SPR2 includes the first third of départements in terms of SPR2 (SP R2 ∈ [2,15[); medium and high SPR2includes the second and last third (SP R2 ∈ [15,29]).

2.5 Results 101

2.5.2 Influence of observable characteristics: demand for better coverage

The effects of observable individual characteristics on the probability of subscribing to better-

SHI are captured through the coefficients γ in the first step of the estimation (Table 2.3). We

find that in our sample, young and healthy (with no chronic disease, CD=0) individuals are

more likely to quit MGEN-SHI. Low income individuals are more likely to take out better-SHI

than high income. Individuals who live in départements where there are few S1 specialists or a

lot of S2 specialists are also more likely to take out better-SHI.

2.5.3 Influence of observable characteristics: moral hazard

We find that better coverage induces significant changes (β1 − β0) in the impacts of regressors,

resulting in heterogeneous moral hazard linked to observable characteristics (Table 2.4): moral

hazard appears to be significantly heterogenous between different levels of income, age, genders,

availibility of S1 specialist. More precisely, the effect of insurance on balance billing consumption

is consistently and significantly decreasing with income: the poor react more to insurance

than the rich. They increase more strongly their proportion of S2 visits and consult more

expensive S2 specialists. Women react also more to a better coverage as concerns their number

of consultations. The increase in quantity of consultations, Q, is 89% higher for women than

for men. However, because the effect on the ratio Q2/Q is also 19% lower for women, it seems

that the quantity effect is mainly due to an increase in S1 visits. Compared to 40-60 years old,

individuals over 60 react more to balance billing coverage. Finally, consistently with our results

in Dormont & Péron (2016), moral hazard on BB/Q is 156% higher (+e21.11) in départements

with low SPR1 and 178% higher (+e25.36) in départements with high SPR2.

2.5.4 Influence of observable characteristics: classical adverse selection and

selection on moral hazard

Classical adverse selection means that patients with a higher balance billing consumption with-

out coverage are more likely to take out better coverage: it can be captured through the

relationship between γ and β0. Selection on moral hazard means that patients with a stronger

102 Chapter2

reaction to balance billing coverage are more likely to take out better coverage: it can be cap-

tured through the relationship between γ and (β1 − β0). Table 2.5 summarizes our findings for

different explanatory variables: it shows that classical adverse selection and moral hazard do

not always go in the same direction.

Selection on moral hazard appears clearly as regards income. Indeed, the impact of income on

the decision to take out better coverage is negative (γ < 0), positive for the use of balance

billing BB/Q with no coverage for it (β0 > 0), and its influence on balance billing decreases

with better coverage (β1 − β0 < 0). We can deduce from this that low income individuals

present a relatively low classical adverse selection but react strongly to health insurance and

are more likely to switch. This findings that low income people react more to an improvement

in coverage seems to us particularly interesting. Assuming that all individuals have the same

marginal rate of substitution between medical services and consumption of other goods, such a

result can be seen as an empirical evidence of Nyman’s interpretation of moral hazard (Nyman

1999, 2003). Poor people would react more to coverage than others because better coverage

not only changes the relative price of consultations with balance billing, but also releases their

budget constraint.

Table 2.5 shows also that individuals living in départements with few S1 specialists show both

classical adverse selection and selection on moral hazard, which explains their high motivation

to switch. On the contrary, old individuals who also consume a lot of balance billing and would

react strongly to health insurance are less likely to switch. The switching costs are probably

too high considering that, for individuals over 60, MGEN premiums are on average lower than

the competition which generally uses age-based premiums.

2.5.5 Heterogeneity in moral hazard depending on unobservable character-

istics

Is moral hazard heterogeneous depending on unobservable characteristics? Is it related to the

decision to quit MGEN-SHI? A simple test of joint significance on the terms of the propensity

score polynomial shows that we have to reject the hypothesis of a homogenous treatment effect

(Table 2.6). Furthermore, the signs of p2 and p3 give us the form of the MTE function depending

2.5 Results 103

on UD. Table 2.7 compares IV estimates, as well as semi-parametric estimates of ATE and MTE

for different values of p. Figure 2.4 plots the semi-parametric MTE depending on UD with 95%

confidence intervals and all covariates at their mean value. Because the common support is

relatively restricted (Figure 2.2), roughly for p included in [0.02,0.35], we cannot interpret the

MTE results for UD > 0.35. Similarly, Figure 2.3 plots parametric MTE depending on UD

with 95% confidence intervals and all covariates at their mean value. Results are very close to

semi-parametric estimates.

The MTE of better health insurance on Q2/Q, BB/Q and BB/Q2 is decreasing in UD. This

shows selection on moral hazard: individuals who are more likely to take out better coverage

have a stronger reaction to health insurance because of unobservable characteristics. We find

the contrary for the MTE of better health insurance on Q: it is increasing in UD: those who

are the less prone to take out better coverage show moral hazard in the number of specialist

consultations only (of any sector, 1 or 2).

To interpret this result, we need to go back to the model specified in equation (2.16). UD

corresponds to quantiles of V . For a given propensity score, the decision to take out better

SHI depends on the value of V (Zγ > V ). The lower V , the higher the probability of choosing

better-SHI. V can be linked with unobservable individual characteristics such as disutility (V1)

of administrative switching costs, belief (V2) that sector 2 doctors provide better quality of

care, or risk aversion (V3). Assuming for simplicity that risk aversion is homogenous across

individuals, the decision depends on V1 − V2: better-SHI subscription is restrained by the

disutility of switching costs (V1) but encouraged by faith in better quality (V2). Following this

interpretation, individuals who are the more prone to switch for better SHI are those with the

stronger faith in the quality of care provided in sector 216.

Our findings give empirical support for such a story: the highest impact of better coverage on

balance billing consumption (BB/Q) is observed for the first switchers. For the first decile of

UD (i.e. of V ), they increase their balance billing per consultation by e111.9 (Table 2.7). Then

16In our specification, Z is by definition uncorrelated with V , U1 and U0, while V can be correlated with theunobservable components, U1 and U0, in the demand for balance billing or for consultations. While there is onlyone V driving the decision to switch, U1 and U0 are different for each of our four variables of interest Q, Q2/Q,BB/Q and BB/Q2.

104 Chapter2

MTE decrease for higher values of UD and become non significant for values between 0.2 and

0.3 (Figure 2.4). Similar results are found for log(Q2/Q), log(BB/Q), and log(BB/Q2), which

are all variables measuring the use of sector 2 consultations.

The reverse is found for log(Q), i.e. the number of specialist consultations (either in sector 1 or

2). For this variable, MTE are increasing with UD as concerns the parametric estimation and

are increasing with UD but generally non significant in the non parametric estimation. In any

case, they are not significant for low values of UD. These individuals do not believe that sector

2 specialists provide better quality of care (or do not value this quality). Hence the disutility

of administrative costs delays their decision to take out better-SHI. Also, the improvement in

coverage has no impact on their use of sector 2 specialists. If any significant impact, it is only

on the number of consultations without distinction between sectors.

Obviously, this interpretation is based on a story on the ‘content’ of the unobservable com-

ponents of the decision to subscribe to better-SHI. Nevertheless, the contrast between the

decreasing profiles of MTE regarding balance billing use (Q2/Q, BB/Q and BB/Q2) and the

increasing or flat profile of MTE regarding the use of specialist consultations provide a strong

support to our econometric approach. In any case, our results are coherent with the expected

effect of heterogeneous beliefs in the quality of sector 2 specialists.

2.6 Conclusion

When insurance is voluntary, some individuals may buy insurance because they expect an

increase in their consumption due to better coverage. Defined as ‘selection on moral hazard’

by Einav et al. (2013), this phenomenon is likely to play a preponderant role in a context of

supplementary health insurance, where subscription is voluntary.

In this paper we investigate the relationships between healthcare use, decision to take out

supplementary health insurance and response to better coverage. We use a model that specifies

individual heterogeneity in demand for healthcare and in moral hazard. We focus on the demand

for specialists who balance bill their patients, i. e. charge them more than the regulated fee

2.6 Conclusion 105

set by NHI. Indeed, the demand for specialists who balance bill relies on preferences and beliefs

in quality of care. Individuals are likely to be heterogeneous in their preferences and beliefs,

while these unobservable characteristics both drive demand for care and decision to take out

SHI, resulting in selection on moral hazard.

In the econometric literature, selection on moral hazard is generally known as ‘essential hetero-

geneity’. Marginal treatment effects estimators have been developed to capture the impact of a

treatment likely to vary across individuals. We use MTE to estimate the causal effect of SHI

coverage on balance billing consumption on a French database of 58,519 individuals observed

in 2012.



subscribe to comprehensive SHI are also those who exhibit stronger moral hazard, i. e. a larger

increase in balance billing per consultation. As concerns the influence of observable character-

istics, we also find that individuals’ income is a determinant of balance billing consumption and

influences the behavioral response to better coverage. Without coverage, the poor consume less

balance billing than the rich but increase their consumption more sharply once covered. They

are also more likely to take out comprehensive coverage.

In a context where SHI is voluntary, the inflationary impact of SHI coverage on balance billing

might be worsened by selection on moral hazard. Our policy conclusions as regards the role of

income are of different nature. The negative effect of income on the demand for balance billing

consultations coupled with its positive effect on moral hazard provides evidence that insurance

plays an important role in terms of access to care for low-income individuals.

106 Chapter2

Tables and Figures

Figure 2.1 – Treatment choice for given propensity score P (Z) and values of disutility UD


Table 2.1 – Number of MGEN-SHI and better-SHI holders and individual characteristics in2012 for individuals with at least one visit to a specialist (Q ≥ 1)

N Women Age Income Chronic Disease% mean (sd) mean (sd) %

MGEN-SHI holders 53,456 72.5 57.7 (15.2) 2,499 (764) 22better-SHI holders 5,063 82∗∗∗ 45.2∗∗∗ (13.3) 2,406∗∗∗ (712) 9.4∗∗∗

∗∗∗ Significantly different from MGEN-SHI holders, p<0.01

MGEN sample: 58,519 individuals with at least one specialist consultation in 2012

Table 2.2 – Number of specialist visits and amount of balance billing in e in 2010 and 2012for individuals with at least one visit to a specialist (Q ≥ 1) in 2010 and 2012

Q Q2 Q2/Q BB BB/Q BB/Q2mean (sd) mean (sd) mean (sd) mean (sd) mean (sd) mean (sd)

In 2010

MGEN-SHI 3.6 (4.6) 1.5 (2.8) 44% (0.43) 35.1 (79.5) 10.4 (12.6) 22.8 (11.6)Future better-SHI 3.7 (4.6) 1.8∗∗∗ (3.0) 52%∗∗∗ (0.43) 47.5∗∗∗ (88.0) 13.2∗∗∗ (13.6) 24.7∗∗∗ (11.6)

In 2012

MGEN-SHI 3.3 (3.4) 1.3 (2.1) 43% (0.43) 32.9 (68.1) 10.5 (13.4) 24.2 (11.7)Better-SHI 3.3 (2.3) 1.7∗∗∗ (2.4) 51%∗∗∗ (0.43) 46.9∗∗∗ (81.5) 13.7∗∗∗ (14.3) 26.1∗∗∗ (12.2)∗∗∗ Significantly different from MGEN-SHI holders, p<0.01


BB/Q2: subsample of 26,557 individuals with at least one S2 specialist consultation in 2010 and 2012

108 Chapter2

Table 2.3 – Effect of covariates and excluded instruments on the probability of taking outbetter coverage (PROBIT)

Pr(QUIT = 1) coef.γ

Women 0.08***Log(income) -0.14***20-40 0.60***40-60 ref.60+ -0.29***CD -0.20***Exp. Phy 0.09***High SPR1 ref.Med SPR1 0.01Low SPR1 0.21***Low SPR2 ref.Med & High SPR2 0.24***Excluded instrumentEarly retirees 1.36***N 58,519


Figure 2.2 – Common support

110 Chapter2

Table 2.4 – Effect of covariates on the consumption of balance billing and on moral hazard

log(Q) log(Q2/Q) log(BB/Q) BB/Q log(BB/Q2)α0 0.70*** -0.68*** -4.40*** -52.63*** 0.26β0

Women 0.10*** -0.01 0.00 0.13 0.05**Log(income) 0.01 0.09*** 0.53*** 6.11*** 0.26***20-40 0.25** -0.00 -0.11 -3.74** -0.24*40-60 ref. ref ref. ref. ref.60+ -0.21*** 0.02* 0.17*** 2.45*** 0.16***CD 0.15*** 0.01 0.17*** 2.68*** 0.13***Exp. Phy 0.16*** 0.14*** 0.81*** 4.22*** 0.16***High SPR1 ref. ref ref. ref. ref.Med SPR1 -0.13*** -0.01 -0.11*** -1.74*** -0.13***Low SPR1 -0.03 0.05*** 0.18*** 0.22 -0.02Low SPR2 ref. ref ref. ref. ref.Med & High SPR2 0.12*** 0.12*** 0.56*** 2.73*** 0.13***(β1 − β0)

Women 0.89*** -0.19*** -0.68*** -8.48*** -0.28*Log(income) -0.08 -0.19*** -1.27*** -15.26*** -0.74***20-40 0.16 -0.15 -0.75 -7.59 0.1140-60 ref. ref ref. ref. ref.60+ 3.01*** 0.69*** 4.35*** 48.34*** 0.47CD 1.19*** -0.12 -0.49 -8.23*** -0.09Exp. Phy -0.02 -0.01 0.15 8.48*** 0.43**High SPR1 ref. ref ref. ref. ref.Med SPR1 0.25** -0.03 -0.01 0.77 0.17Low SPR1 0.07 0.22*** 1.56*** 21.11*** 0.69***Low SPR2 ref. ref ref. ref. ref.Med & High SPR2 0.39* 0.27*** 1.78*** 25.36*** 0.76***N 58,519 58,519 58,519 58,519 33,332


Table 2.5 – Obervables: summary of relationships between probability of switching, demandfor S2 specialists without coverage and moral hazard - average balance billing per consultation(BB/Q)

Switch Demand for BB Moral hazardγ β0 (β1 − β0)

Women + + -Income - + -60+ - + +CD - + NSExp. phy. + + NSLow SPR1 + + +High SPR2 + + +

Table 2.6 – Polynomial coefficients and joint test of significance

log(Q) log(Q2/Q) log(BB/Q) BB/Q log(BB/Q2)p -6.02*** 2.63*** 17.41*** 241.66*** 10.80***p2 16.20*** -3.74** -27.20*** -433.62*** -16.93***p3 -14.17*** 3.05** 21.89*** 325.62*** 12.12**

chi-square statistic 14.50 12.22 25.79 56.76 19.50p-value 0.002 0.007 0.000 0.000 0.000

112 Chapter2

Table 2.7 – Capturing Moral hazard and the effect of unobservables: OLS, IV, empirical ATEand semi-parametric MTE

log(Q) log(Q2/Q) log(BB/Q) BB/Q log(BB/Q2)OLS 0.02** 0.04*** 0.21*** 2.03*** 0.07***IV -0.03 0.04 0.19 1.29 -0.06

Empirical ATE 0.72 0.56*** 3.21*** 30.22* 0.63

MTE p=0.1 -0.97 0.98** 7.04** 111.91** 3.69**

lower bound -2.56 0.34 3.76 81.89 1.13upper bound 0.62 1.62 10.33 141.94 6.24

p=0.2 1.15** 0.43** 2.23** 23.40** 0.48

lower bound 0.05 0.09 0.49 1.78 -0.54upper bound 2.24 0.76 3.96 45.01 1.50

p=0.3 2.58* 0.43 0.15 25.99 0.40

lower bound -0.04 -0.11 -0.10 -37.08 -1.97upper bound 5.21 0.98 0.39 89.05 2.77

Empirical ATE: computed by STATA program ‘margte’ on the common support only


Figure 2.3 – Parametric MTE - log(Q), log(Q2/Q), log(BB/Q), BB/Q, log(BB/Q2)

114 Chapter2

Figure 2.4 – Semi-parametric MTE - log(Q), log(Q2/Q), log(BB/Q), BB/Q, log(BB/Q2)


Figure 2.5 – Empirical ATE on log(BB/Q)

Chapter 3

Supplementary Health Insurance:

are age-based premiums fair?

3.1 Introduction

In France, age pricing is widespread in the supplementary health insurance (SHI) market. The

French system is a mixed public/private health insurance system where private insurers are al-

lowed to provide supplementary coverage. 94% of the French population is actually covered by

a SHI contract and private insurers finance to the amount of 14% of medical expenses. Histor-

ically, health insurance coverage was provided by not-for-profit insurers, the ‘mutuelles’. They

relied on solidarity principles, stated in particular by Bourgeois (1912), to guarantee horizontal

equity between high and low risks. Since the enactment of a National health insurance (NHI)

system in 1946, the role of the mutuelles has changed; they now provide SHI coverage and cover

co-payments and medical goods and services out of the NHI benefit package. During a long

period, most SHI contracts had very simple features: a unique contract with uniform premiums,

i.e. a flat fee, regardless of the individuals’ characteristics or a premium proportional to the

individual’s income. Recently, the constant increase in healthcare expenditures together with a

freeze of public coverage has made the SHI market very attractive. New entrants adopt aggres-

sive strategies by providing tailor-made contracts with actuarial premiums, which depend on

I am very thankful to Marc Fleurbaey for his support, his expertise and his thoughtful comments in thecourse of this project.

118 Chapter3

the individual risk. The mutuelles are experiencing the ‘adverse selection death-spiral’ (Roth-

schild & Stiglitz 1976, Cutler et al. 1997): they lose their low-risk clients attracted by lower

premiums. Therefore, a higher share of high-risk in a mutuelle’s portfolio leads to an increase in

premiums and speeds up the loss of low-risk. To survive, the mutuelles are keeping away from

their founding principles of equal access and solidarity. They give up on uniform premiums and

price their contracts closer to the individual risk of illness.

In France, setting premiums on individuals’ previous healthcare expenditures is forbidden1 and

the use of medical questionnaires is strongly discouraged by fiscal penalties. Therefore, the

mutuelles use age as a predictor for individuals’ risk. In 2010, 90% of individual insurance

contracts provided by mutuelles were priced with age-based premiums, having been only 66%

in 2005 (Le Palud 2013). For most of the contracts, premiums for a 75 years old are on average

three times higher than for a 20 years old (DREES 2016). Fairness issues are not only a side-

effect of market dynamics but also a political argument. In France, it is especially critical for

mutuelles for which each major decision has to be voted by an assembly of representative of

the enrollees. Indeed, the mutuelles have to convince their stakeholders that moving towards

premiums adjusted on individual’s risk will not go too far against their founding principles in

terms of risk sharing and access to insurance. Note that although the French SHI market has

specific features, the questions raised by a voluntary SHI financed through age-based premiums

find an echo on several health insurance systems such as Belgium, Switzerland, the Netherlands

or the USA with Medigap.

Do age-based premiums endanger solidarity? To investigate this question, we propose to focus

on healthcare payments bear by individuals. A given use of healthcare services is linked with

a given level of healthcare costs. We call ‘healthcare payments’ what the individual ultimately

pays, i.e. health insurance premiums and out-of-pocket (OOP) payments. In mutuelles’ found-

ing principles, solidarity was expressed through two dimensions: (i) to which extent healthcare

payments are disconnected from healthcare use; (ii) how healthcare payments bear on individ-

uals’ available income. How age-based premiums impact these two dimensions? Is the impact

different in a context of voluntary insurance?

1Loi n° 89-1009 du 31 décembre 1989, Loi Évin

3.1 Introduction 119

In order to focus on the effect of premiums, let’s consider a very simple world were individuals

can purchase a unique contract with standardized coverage. First, healthcare payments can be

more or less disconnected from healthcare costs depending on the way premiums are defined.

Because consumption of healthcare increases with age, age-based premiums are necessarily closer

to individuals’ healthcare costs than uniform premiums. However it is unclear how age-based

premiums perform compared to income-based premiums or other forms of premiums closely

related to the individual risk. Interestingly, compared to France, the USA are experiencing

quite an opposite change. The USA increase regulation in the private health insurance market

and use age-based premiums to move towards a system with a higher degree of solidarity. A

paper by Stone (1993), "The struggle for the soul of health insurance", deplored the extinction of

traditional not-for-profit insurers in favour of insurance companies who discriminate according

to risk of illness. Unaffordable actuarial premiums left the sick without any health insurance

coverage. The main goal of the Affordable Care Act (ACA) is precisely to share the financial

risk due to illness to a great extent. The ACA bans medical underwriting, a practice that highly

disadvantages sick people, and endorses a community rating only adjusted by age and gender. In

this context, compared to medical underwriting, age pricing is regarded as a movement toward

more community rating. Note that the effect of age on premiums is limited since the Medicare

program covers the elderly (65+) and is funded through contributions depending on income,

mainly paid by workers. The second dimension of solidarity is related to income inequalities.

Precisely, how age-based premiums bear on individuals’ income. The answer is not clear either.

It depends on the correlation between age, income and healthcare use. For instance, when the

Mutuelle Générale de l’Éducation Nationale (MGEN) decided to increase the rate of income-

based premiums for retirees, the main argument was that retirees were generally wealthier so

they could contribute more (3.56% of their income vs 2.97%). Finally, the impact of age-

based premiums depends on whether insurance is mandatory or voluntary. When insurance is

voluntary, individuals can choose not to be insured, especially if premiums are too expensive

compared to their expected healthcare expenditures. This impacts the distribution of healthcare

payments in two ways. First, through the effect of adverse selection, premiums paid by those

who remain insured are likely to increase. Second, those who decide to remain uninsured bear

the risk of facing important OOP payments.

120 Chapter3

To our knowledge, the impact of premiums in the context of voluntary SHI has not been studied

in the literature. Obviously, health insurance has been the focus of an important number of

theoretical and empirical contributions. However, because the literature usually considers the

NHI level, results are difficult to generalize to the SHI context. Indeed, SHI is meant to cover

a different type of risk than NHI. Especially in the French context where NHI covers inpatient

care and does not charge co-pays for patients with chronic disease, expenditures covered by SHI

are likely to be less extreme, possibly more predictable for the individuals too. For the same

reasons, adverse selection phenomena, well documented in the case of basic health insurance,

are likely to be different in a context of a mixed system with mandatory NHI and voluntary SHI.

Furthermore, because of a lack of data, we have seldom knowledge about the distribution of

healthcare expenditures effectively covered by SHI. Correlations between SHI reimbursements,

age, income and health condition, which are critical to understand the distributional impact of

age-based premiums, have not been documented either.

To bridge this gap, we exploit an original database of 87,110 individuals, aged from 25 to 90

years-old, for whom we observe their SHI reimbursements and final OOP. We adopt an empirical

approach and use simulation methods to compare the impact of age-based premiums with other

regimes and illustrate adverse selection phenomena when insurance is voluntary. Simulations are

calibrated with data specific to the SHI context. We focus on ex post outcomes to fully take into

account the specificity of SHI in terms of distribution of expenditures and correlations with age,

income and health status. In line with the literature on equity in healthcare financing (Wagstaff

& Van Doorslaer 2000), we use concentration curves and inequality indexes to measure the

impact of premiums on income distribution. An original contribution of our paper is to adapt

these tools to measure the impact of premiums on transfers between low and high healthcare

users.

3.1.1 Aim of the paper, methodological framework and contributions

In the context of voluntary SHI, this paper aims at measuring how age-based premiums impact

the extent of risk sharing between low and high users and the extent of income redistribution

between low and high income groups. We compare their impact with other regimes of premiums:

from pure CR to actuarially fair premiums or income-based contributions.


We focus on expenditures meant to be covered by SHI, i.e. the part of healthcare expenditures

not covered by NHI. We consider a simple framework where individuals have only the choice to

subscribe to SHI or not. There is only one contract available with the same level of coverage

and the same regime of premiums for all policyholders. Firstly, we use simulations to compute

different types of premium (uniform, age-based, income-based, income-based adjusted with age,

medical underwriting and experience rating), predict whether individuals will take-out SHI or

not, calculate their subsequent healthcare payments (premiums plus OOP payments). Secondly,

we use concentration curves to derive equity indexes on risk sharing and vertical equity from the

simulated outputs. We also allow for possible dynamic adverse selection effects due to the fact

that some individuals can choose not to buy SHI when insurance is voluntary. The simulation is

calibrated using individual panel data from a French supplementary health insurer, the Mutuelle

Générale de l’Éducation Nationale (MGEN). Our database stems from the administrative claims

of 87,110 individuals, aged from 25 to 90 years-old, who are all covered by the same SHI contract

from January 2010 to December 2012. Our data provide socio-economic and health status

information as well as supplementary healthcare expenditures (SHE), supplementary health

insurance reimbursements (SHIR) and OOP payments.

Our choice to focus only on supplementary healthcare expenditures is motivated by two reasons.

The first reason is that the political debate in France about coverage inequalities, the extent

of risk sharing and how premiums weight on households’ budget concerns SHI. Although SHI

covers a relatively limited part of total healthcare expenditure (13%), it is considered as essential

in access to care2. Supplementary health insurers themselves, especially the mutuelles, which

are not-for-profit and headed by an elected board, are concerned about the fairness of their

price strategy. On the one hand, market’s dynamic force them to price their contracts closer

to the individual risk. On the other hand, they have to convince their stakeholders that this

will not endanger their founding principles based on solidarity and equal access. The second

reason is practical: data availability dictates our decision to focus only on SHI. Although our

database includes total healthcare expenditures and NHI reimbursements, data are missing on

hospital expenditures which are mostly covered by NHI. On the contrary, available databases

with comprehensive information on NHI reimbursements do not include SHI reimbursements2This idea has led to the creation of a free SHI for very low income individuals in 2000, the Couverture

Maladie Universelle Complémentaire (CMU-C)

122 Chapter3

and final OOP payments. This would preclude a complete analysis of the whole health insurance

system (NHI plus SHI).3

We use a simple framework where only one contract is provided by one insurer with the same

level of coverage and the same regime of premiums for every insured. Individuals have only

the choice to be insured or not. We also assume null profits: because they are not-for-profit

organizations, mutuelles’s objective is to break even, not make profits. A load factor is however

charged by the insurer to cover administrative costs. There is no competition between insurers in

our model, neither on premiums or level of coverage. This simplification allows us to focus on the

effect of age-based premiums on individuals’ healthcare payments, independently from the effects

driven by coverage choices or imperfect competition. Several papers, that we present in more

details in the next section, have already simulated the effects of competition on coverage (Handel

et al. 2015) and premiums (Ericson & Starc 2015). A theoretical contribution by Goulão (2015)

also studies the case where individuals have the choice between different types of premium.

Furthermore, assuming a standardized contract is not very far from the reality of the French

SHI market. Although the extent of coverage can vary regarding medical services outside the

NHI benefit package (such as balance billing or optical devices), contracts are very homogeneous

for coverage of NHI co-pays. Indeed, insurers benefit from fiscal advantages if their contracts

are certified as a ‘contrat solidaire et responsable’ by the French government. This especially

implies full coverage for NHI co-pays on hospital and ambulatory care.

In our framework where insurance is voluntary insurance and contracts are standardized, we

model the decision to take out SHI considering individuals as utility maximizers who face a

distribution of expected health expenditure which depends on their characteristics. Simulations’

results in terms of level of premiums or number of uninsured will depend strongly on the

specificity of our sample and on the assumptions we make in terms of individuals’ knowledge

about their risk, their risk aversion or the form of their utility function. The accuracy of our

results in terms of prediction if one of these schemes were implemented is therefore probably

relatively low. However, precisely because we run simulations on the same sample, we are

3Note that because NHI in France is mandatory and universal and SHI is not a substitute to public coverage,we can analyze the impact of SHI premiums separately from the redistribution implied by the NHI. There areindeed no adverse selection issues on the NHI, as it could be the case in Germany for instance where individualscan opt out from NHI and buy private coverage instead (Panthöfer 2016).


able to compare different types of premiums, evaluate their impact on risk sharing and income

redistribution and understand the consequences of adverse selection.

As we will justify it further, we focus on ex-post outcomes: how the way premiums are defined

will impact the distribution of healthcare payments (premium + OOP payments) between low

and high users and low and high income. Our approach departs from the welfarist approach

considered in many papers devoted to health insurance (Blomqvist & Horn 1984, Rochet 1991,

Cremer & Pestieau 1996, Henriet & Rochet 1998, Petretto 1999). Indeed, these papers consider

the effect of health insurance on social welfare without further analysis on its distributional

impact. Furthermore, their analysis is usually performed ex ante, based on individuals’ expected

utilities, rather than ex post, once the consumption of healthcare is realized and known. As

advocated by Fleurbaey (2008), the ex post perspective takes into account more information

than the ex ante perspective. Indeed, in a context of voluntary insurance, the ex post outcome in

terms of healthcare payments (premium + OOP payments) will reflect both individuals’ ex ante

appreciation of risk (through SHI subscription) and the realization of healthcare expenditures.

Because we focus on ex post distributional impact of SHI, inequality indexes appear to be ap-

propriate tools. In particular, concentration curves have been widely used to measure the effect

of health insurance payments on income distribution (Wagstaff & Van Doorslaer 2000). They

have the attractive advantage to represent in the same diagram income as well as healthcare

payments distributions. From these curves, we are also able to derive several equity indexes

that can be used to compare different regimes of premiums. These measures focus on vertical

equity, on how premium regulation makes payments more or less progressive and contribute

to reduce, or increase, income inequalities. It is also possible to adapt concentration curves

to measure the extent of redistribution between low users and high users of healthcare. This

way, we are able to explicitly distinguish the impact of age-based premiums on risk sharing and

vertical equity in our analysis. Note that Aronson et al. (1994) suggest to decompose the re-

distribution effect into three components: pure vertical equity, reranking and horizontal equity.

We argue that the measure used is not satisfying in terms of practical use and interpretation.

Indeed, as noted by Wagstaff & Van Doorslaer (2000), even though the theoretical distinction

between reranking (treatment of unequals) and horizontal equity (treatment of equals) is valid,

124 Chapter3

the empirical distinction is difficult and somewhat artificial because it depends eventually on

the definition income groups’ width. Furthermore, we consider that the concept of horizontal

equity as defined by Aronson et al. (1994) is intrinsically different from what we define as ‘risk

sharing’, i.e. the redistribution between low and high healthcare users. Indeed, measuring ‘hor-

izontal equity’ implies to remain within the general framework of income distribution, taking

the goal of redistributing income as granted. Yet, as noted previously, fairness of healthcare

payments may also be considered from the narrower spectra of risk sharing, letting voluntarily

income inequalities not due to differences in health aside.

This paper contributes to the economic literature on health insurance on three different ways.

First, the analysis of an original database on supplementary healthcare expenditures and OOP

payments characterizes the specificity of SHI in terms of distribution of expenditures and cor-

relations with age, income and health status. Second, in the SHI context, our simulations

illustrate how age-based premiums deal with adverse selection and impact the ex post distribu-

tion of healthcare payments. Third, we propose a methodological contribution to the literature

on equity in healthcare financing by using concentration curves to measure the extent of redis-

tribution not only between income groups but also between low and high healthcare users.

Based on our simulations, we derive three results on the impact of age-based premiums in the

SHI market: (i) in a context of voluntary SHI, age-based premiums is the best solution to

preserve risk sharing; (ii) however, they achieve risk sharing at the expense of vertical equity;

(iii) the absence of a mandate limits the impact of SHI on risk sharing and vertical equity,

especially when premiums are based on a form of community rating.

The paper is organized as follows. In section 3.2, we define ‘healthcare payments’ and review

the literature focusing on the impact on efficiency and fairness of health insurance premiums.

Section 3.3 presents the indexes we use to measure risk sharing and vertical equity. Section 3.4

describes how we model individuals’ decision to take out SHI, compute premiums and simulate

individuals’ healthcare payments. Section 3.5 presents the data on which our simulations are

based and descriptive statistics on SHE, SHIR and OOP payments distribution from our sample.

Section 3.6 summarizes the results stemmed from the simulations. Section 3.7 concludes.

3.2 How to define and design fair healthcare payments? 125

3.2 How to define and design fair healthcare payments?

In this section, we define ‘healthcare payments’ and compare the different types of health

insurance premiums. We also review the economic literature on health insurance focusing on

the design of healthcare payments and its consequences in terms of efficiency and fairness.

3.2.1 Healthcare payments: concepts and definitions

We previously defined ‘healthcare payments’ as the amount an individual will ultimately pay

for healthcare, which is the sum of her health insurance premium and OOP payments.

A health insurance premium is a payment made to an insurer in order to be covered against

future healthcare costs. The payment is made ‘ex ante’, i.e. before the individual consumes

healthcare. Similarly to all other types of insurance, the financial risk, in this case related to

healthcare consumption, is shared with all other individuals who took out insurance and joined

the ‘pool’. Indeed, by paying a premium, the enrolle agrees that her contribution will be used

to socially finance the pool’s healthcare expenditures. Health insurance premiums can be set in

different ways. Two principles are usually opposed: ‘community rating’ and ‘actuarial fairness’.

Community rating (CR) implies that contributions are disconnected from individual risk and

rather depend on the average risk of the pool. On the contrary, actuarial fairness requires the

premium to be as close as possible to the individual’s risk, measured ex ante by the expectancy

of her healthcare expenditures. Consequently, the extent of ‘risk sharing’, i.e. the extent of ex

post transfers between the ‘low-users’ and the ‘high-users’ of healthcare among the pool, will

be more important with CR than with actuarially fair premiums. It is worth noting though

that insurance always implies a form of risk sharing, even when the premium is based on the

individual’s risk. Indeed, ex ante, when the premium is paid, the realization of healthcare

consumption is still uncertain. Among those who paid a higher premium due to their higher

risk, some will be low-users ex post and will subsidize high-users.

Theoretically, one can draw a continuum of premiums from total to limited risk sharing. ‘Uni-

form premiums’ would be the purest form of CR. A uniform premium is a flat fee, an equal

126 Chapter3

contribution paid by all individuals whom join the pool, regardless of their own risk. The pre-

mium therefore depends on the expected average health insurance reimbursements conditional

to the pool. ‘Age-based premiums’ lie further on the continuum. Premiums will indeed in-

crease with age because older individuals present a higher risk to be high-users of healthcare.

Age-based premiums are usually classified as a form of ‘adjusted community rating’. Indeed,

although linked to individual risk, age-based premiums also imply a form of CR among the pool

of individuals who belong to the same age-group. Adjusted CR can also use gender or location

to define premiums. Obviously, as criteria become more and more related to individual risk,

the ‘adjusted pool’ shrinks as does risk sharing. At the right-hand side of the continuum, where

risk sharing is very limited, insurers would use information about previous and current diseases,

known as ‘medical underwriting’ or use directly previous healthcare consumption, known as

‘experience rating’. We are therefore closer to the actuarial fairness principle, where premiums

depend on individual risk rather that on the average risk of the pool.

‘Income-based premiums’ stand apart from this continuum. Indeed, income is not used here

as a risk predictor4. The rationale of income-based premiums is rather related to how health

insurance premiums weight on individuals’ budget. Rather than risk sharing, the emphasis is

indeed on ‘vertical equity’. As regards healthcare financing, vertical equity states that indi-

viduals with unequal income should contribute unequally to healthcare payments. Precisely,

vertical equity implies that payments should be at least proportional to income (equivalent to a

uniform tax rate) or progressive (equivalent to an increasing marginal rate). It is worth noting

that vertical equity and risk sharing can be conflicting objectives. Indeed, whereas risk sharing

is maximized when premiums are uniform, the ‘premium to income ratio’ (PIR) decreases with

income and consequently the poor contribute relatively more than the rich: uniform premiums

are regressive and do not achieve vertical equity. Moreover, if the rich consume more healthcare

than the poor, income-based contributions will limit transfers from low to high healthcare users.

When premium are based on income, the contribution can either takes the form of a uniform

rate – the PIR will therefore be constant with income (proportional payments) – or be set with

an increasing marginal rate (progressive payments).

4Although income-based premiums are actually similar to adjusted CR: premiums depend on the averageexpenditures of the pool and are adjusted to individuals’ income


Contrary to health insurance premiums, which are defined ex ante, the other component of

healthcare payments occurs ex post: OOP payments depend on the realized healthcare con-

sumption, and are entirely borne by the individual. OOP payments correspond to the share of

healthcare expenditures not covered by the insurance contract: general deductibles (insurance

reimbursements only start after a certain amount of expenditures), co-payments (a fixed or vari-

able share of the price of healthcare is not covered) or costs of medical goods not included in the

benefit package. Formally, OOP payments equal the difference between healthcare expenditures

and health insurance reimbursements.

We investigate the following question: in a context of voluntary insurance, do age-premiums

guarantee a fair distribution of healthcare payments? Note that when insurance is mandatory

and covers a standardized benefit package, the respective impacts on risk sharing and vertical

equity of health insurance premiums and OOP payments are disconnected and can be analyzed

separately. Indeed, if the whole population benefits from the same coverage, the way premiums

are defined has only an impact ex ante, before healthcare consumption. However when insurance

is voluntary, the way premiums are defined is likely to influence individuals in their decision to

take out health insurance. In this case, ex post OOP payments will be directly related to the

ex ante payment of the premium. When insurance is voluntary, it is therefore critical to adopt

an ex post approach, after healthcare use is realized, that considers the distributional impact

of both health insurance premiums and OOP payments.

3.2.2 Literature: efficiency and fairness of healthcare payments

The political debate on how to define health insurance premiums is a mix of pure efficiency

arguments and ethical considerations. The economic literature, either normative or positive,

has mainly focused on efficiency issues, mostly investigating the welfare consequences of health

insurance premiums by taking into account moral hazard behavior, adverse selection phenom-

ena, reclassification risk or imperfect competition. A large part of the literature also aims at

justifying income-based premiums in social health insurance systems on efficiency grounds. The

specific impact of age-based premiums is seldom analyzed, except in recent contributions that

followed the implementation of the ACA in the USA. As regards fairness, the literature on so-

cial choice acknowledges that different conceptions of a fair premium coexist. Empirical studies

128 Chapter3

which attempt to measure the redistributive effect of health insurance premiums are quite lim-

ited and do not take into account the extent of redistribution between low and high healthcare

users. More importantly, the distributional impact of premiums in a context of voluntary SHI

has not been studied.

According to Zweifel & Breuer (2006), uniform premiums harm efficiency since they preclude

contracts’ optimality in terms of ex ante and ex post moral hazard. Indeed, Zeckhauser (1970)

and Blomqvist & Johansson (1997) show that a contract with a cost-sharing rule (i.e. level of

deductibles and co-pays) that is non-linear in healthcare expenditure is generally optimal to

limit moral hazard. For instance the rate of co-pays should decline after a certain amount of

expenditures. This implies that contract design, in terms of coverage and ultimately in terms

of premiums, must depend on individual characteristics; which is impossible to implement

with uniform premiums. Rather than uniform premiums, Zweifel & Breuer (2006) therefore

recommend to use actuarial premiums, even for NHI contributions. Indeed, premiums based

on individual’s risk and previous consumption reward those who invest in prevention and make

effort to limit their healthcare expenditures.

Several papers attempt to estimate the adverse effect of community rating when it is imple-

mented on a market without mandate. They compare the percentage of uninsured, usually

across different states in the United States characterized by different rules for setting premi-

ums. A first paper by Buchmueller & Dinardo (2002) does not report any evidence of such

a death-spiral in the American market for ‘small businesses’ employer-based health insurance.

Using data between 1987 and 1996, they do not find significant differences in the percentage of

uninsured between the state of New-York where CR has been implemented in 1993 and other

states where regulation on premiums was weaker. Herring & Pauly (2006) also find small dif-

ferences in the employer-based market using more recent data but explain this result by the

fact that, even when considering unregulated markets, pooling might be relatively important

and makes unregulated and regulated markets eventually closer in terms of outcomes (coverage

rates, type of contracts and premiums) than expected. However, evidence of adverse effects of

community rating seems to be more striking in the individual market. Using US data from a

national survey, Sasso & Lurie (2009) report that "young and healthy people were 20 to 30%

more likely to be uninsured as a result of community rating".


The Affordable Care Act gave rise to a literature focusing on the impact of different forms of

premiums on behaviors in a competitive health insurance market. These contributions especially

enlighten interactions between premium regulation and market’s dynamic. Handel et al. (2015)

investigate the welfare implications of different regimes of premium (namely, CR or actuarial

fairness) in a competitive market, when insurance is mandatory. They build a simulated market

exchange where two contracts are offered: one with a 10% co-pay the other one with a 40%

co-pay. Individuals are not allowed to opt-out and must choose among the available contracts,

the whole population is therefore at least partially insured. The authors use employer-based

health insurance data to estimate risk distributions faced by consumers. They can allow for

heterogeneous risk aversion and estimate its correlation with individuals’ objective risks. They

target two sources of inefficiencies: adverse selection and reclassification risk. Adverse selection

is likely to occur when regulation imposes a form of community rating: due to the adverse

selection death spiral, the generous contract disappears and individuals have no choice but to

be covered with high co-payments. Reclassification risk however is specific to actuarial premiums

because individuals bear the risk of an increase in premium if their health state deteriorates.

The simulation model gives, for each type of premiums, the contract each individual will choose.

The authors are then able to compute the expected utility of an individual, starting at age 25

until 65, given her risk aversion and risk profile. To measure the welfare difference between two

regimes of premiums, x and x′, they define the fixed yearly payment the individual should receive

under regime x to be indifferent between regimes x and x′. The authors find that, although

the adverse selection cost, in terms of social welfare, can be important with community rating,

the reclassification risk cost, induced by actuarial premiums, is five times higher. Interestingly,

age-based premiums do not seem to improve welfare compared to uniform premiums. Age-based

premiums undo transfers from the younger to the older groups while not avoiding the adverse

selection death spiral: the contract with generous coverage still disappears even for younger age

groups.

Ericson & Starc (2015) also use a simulated exchange market to estimate the welfare effects of

premium regulation. Unlike Handel et al. (2015) however, they release the perfect competition

assumption and allow insurers to earn different markups according to consumers’ price sensi-

tivity. In particular, the authors assume that younger consumers are twice as price sensitive

130 Chapter3

as older consumers. Consequently, in the absence of a strict regulation on premiums, older

consumers are likely to pay higher premiums due to higher markups. The authors conclude

that restrictions on age-based pricing, from pure CR to bounded ratios, not only increase trans-

fers from the younger to the older groups but also lower overall markups, increasing consumer

and overall surplus. However, the authors also insist on the adverse consequences of regulation

when insurance is voluntary: the marginal consumer, highly price-sensitive, is likely to opt-out

leading on the market consumers with a low price-sensitivity on whom insurers will impose high

markups. As a result, Ericson & Starc (2015) state that "a weak or absent mandate may negate

the consumer surplus gains achieved from modified community rating". As a matter of fact, this

literature stresses that the impact of premium regulation can be strongly modified when health

insurance is voluntary in a competitive market. In particular, the potential adverse effects of

CR on risk sharing cannot be ignored.

Although income-based premiums are widespread in European social insurance systems, the

idea that health insurance should imply pro-poor transfers is far from consensual. Atkinson &

Stiglitz (1976) argue that introducing redistributive instruments on top of income taxation is

usually redundant or even inefficient. Breyer & Haufler (2000) further confirm that separat-

ing health insurance from income redistribution would yield substantial efficiency gains. On

the contrary, there is an extensive literature advocating income-based contributions for social

health insurance. Adopting a welfare perspective, several papers show that when low-income

individuals also face higher risks a health insurance system that combines redistribution from

the rich to the poor and from the healthy to the sick is better in terms of welfare than a pure

optimal income tax (Blomqvist & Horn 1984, Rochet 1991, Cremer & Pestieau 1996, Henriet &

Rochet 1998, Petretto 1999). Kifmann (2005) adopts a constitutional perspective to show that

income-based premiums are likely to be socially accepted, even by high-income groups, provided

that individuals face a reclassification risk in an alternative private market (their premium in-

creases as they become sicker) and income inequalities are moderate. According to Kifmann

(2005), this could explain why the US, where inequalities are more extreme than in most Eu-

ropean countries, are very reluctant to endorse a universal system financed through taxes. A

theoretical paper by Goulão (2015) shows that when individuals have the choice between a

health insurance contract with income-based premiums and another contract with actuarially


fair premiums, some individuals are still willing to participate to the income-based premiums

contract. Another result is that the presence of a contract with income-based premiums can

increase efficiency in the health insurance market. Indeed, high risk individuals tend to prefer

income-based premiums and therefore signal themselves as high risk. This reduces information

asymmetry in the market.

In terms of political acceptability, fairness arguments may be as important as efficiency consid-

erations. The first difficulty however is to define from a normative point of view what a fair

premium should be. Stone (1993) wrote that individuals are not responsible for there medical

expenses and so there is nothing fair about making the sick contribute more and only uniform

premiums can guarantee fairness in healthcare financing. Interestingly, when advocating the

efficiency of actuarial premiums, Zweifel & Breuer (2006) also refer to ethical consideration

arguing that uniform premiums are unfair because they yield transfer from healthy but poor

individuals to individuals likely to be wealthier and heavy users of medical care. As they state:

"a healthy young worker would subsidize a wealthy older manager who is a heavy user of medical

services". Furthermore, Pauly (1984) argues that because individuals are partly responsible for

their medical expenses, due to their health behavior or overconsumption of health care, actuarial

premiums are more equitable than uniform premiums. These apparent conflicting statements

are in a sense all acceptable definition of fairness, they are just built on different ethical grounds

that eventually refer to different conceptions of social justice.

As noted by Fleurbaey & Schokkaert (2011) though, "there is a widespread conviction that

health care is not a commodity like other commodities, because health care expenditures are

largely imposed on individuals, rather than freely chosen. It follows that the financial burden

should not disproportionately rest on those who suffer from illness". According to Culyer (n.d.),

decoupling healthcare use from healthcare payments also ensures that health expenditures will

not threaten the ability of households to purchase other goods with the same kind of ethical

status such as education or housing. This pleads for the idea that health insurance should at

least achieve horizontal equity, meaning that individuals with equal ability to pay eventually

end up making equal payments. There is no consensus however on the extent of horizontal

equity. As regards healthcare financing, perfect horizontal equity is achieved when healthcare

132 Chapter3

payments are entirely disconnected from healthcare expenditures, i.e. when risk sharing as we

defined it previously is maximized. However, is this situation fair when differences in health care

consumption are due to individual’s behavior or preferences? The recent literature on equity,

responsibility and compensation (Fleurbaey 2008, Roemer 2009) offers a useful framework to

analyze the extent of solidarity that should be achieved in terms of healthcare payments. Espe-

cially, Fleurbaey & Schokkaert (2009) measure inequalities in health and healthcare consump-

tion by introducing a distinction between explanatory variables leading to ‘ethically legitimate

inequalities’, that engage individuals’ liability, and those leading to ‘ethically illegitimate in-

equalities’ that should call for compensation. Schokkaert & Van de Voorde (2004) also used the

fair allocation framework to differentiate legitimate from illegitimate factors in risk-adjustment

models. Eventually, the criteria used to define premiums, such as age, gender, income, medical

history, smoking behavior, should reflect what society considers as acceptable or unacceptable

in terms of inequalities in healthcare payments and in which extent health insurance should

compensate for it. Theoretically, age and sex would appear as ‘illegitimate factors’, for which

it seems hard to engage individuals’ responsibility, and health insurance should compensate

for subsequent inequalities in healthcare use. In practice however, the conception of what is

acceptable or not varies across countries and time. Premiums increasing with age seem to be

easily accepted, or at least widely adopted by both European and American health insurance

markets. Setting different prices for men and women has been considered as a discriminatory

practice by the European Union (EU) and gender-based premium have been forbidden on EU

health insurance markets since 2012.5 On the contrary in the USA, the ACA allows insurers to

adjust premiums on age, gender as well as on smoking behavior.

There is no ethical consensus either on whether healthcare payments should increase with in-

come. This principle is often referred to as vertical equity: households with unequal ability

to pay should unequally contribute to healthcare finance. This conception of equity is also

close to the venerable Marxist principle that originally founded most of the European social

insurance systems: ‘To each according to her needs, from each according to her ability to pay’.

Even though there is no undisputable ethical principle to defend this conception, the fact that

income-based premiums are widespread in social health insurance systems seems to express

5The decision was following the Court’s judgement on 1st March 2011 in the Test-Achats case (C-236/09)


a political and social concern about how healthcare payments weight in households’ budgets.

Furthermore, in multiple payers systems where premiums are not related to income, as it is the

case in Switzerland or in the American market exchange for instance, low-income individuals

usually benefit from public subsidies.

As regards the empirical measure of inequality in healthcare payments and of equity in financing

healthcare, methodological tools have been used to assess and compare the distributional effects

of health insurance on income. This approach is derived from the literature on income inequal-

ities and is based on the use of concentration curves; see Wagstaff & Van Doorslaer (2000)

and De Graeve & Van Ourti (2003) for a review on methodology and results. Early estimations

for France have shown the regressive impact of SHI (Lachaud & Rochaix (1995)). However, the

data used for this study date from 1984 and are based on individuals’ declaration about the

premium they pay and their annual OOP payments. More recently, Duval et al. (2012) have

investigated the nature of transfers induced by both NHI and SHI in France and conclude that

premiums in the SHI market limit the redistribution between low and high risks. However, this

study suffers from several drawbacks. First, the study is not focused on age-based premiums

and it is actually impossible to disentangle in their results the respective effect of different types

of premiums. Second, there are concerns about the quality of the data they use. They do not

have access to comprehensive data on health insurance coverage and therefore use imputation

methods to reconstruct SHI reimbursements and OOP payments. One of the consequences of

imputation, besides the risk of approximations and measurement errors, is that the analysis is

only performed on the deciles of the healthcare expenditures distribution. Therefore the study

does not take into account the top of the distribution, where healthcare payments can be ex-

tremely important for a small number of individuals. Finally, the extent of redistribution is

measured for specific groups of individuals (by income decile, age or health status) through a

ratio contribution/benefit that ignores the correlations between risk, healthcare expenditures

and income and makes the impact of age-based premiums on risk sharing and vertical equity

unclear.

Our paper contributes to the literature by measuring the distributional impact of age-based

premiums in a context of voluntary SHI. We adopt an empirical approach and use simulation

134 Chapter3

methods to compare the impact of age-based premiums with other regimes. Simulations are

calibrated with data specific to the SHI context: we exploit an original database of 87,110

individuals, aged from 25 to 90 years-old, for whom we observe their SHI reimbursements and

final OOP. We focus on ex post outcomes to fully take into account the specificity of SHI in

terms of distribution of expenditures and correlations with age, income and health status. We

use concentration curves and inequality indexes to measure the impact of premiums on income

distribution. An original contribution of our paper is to adapt these tools to measure the impact

of premiums on transfers between low and high healthcare users.

3.3 Measuring the extent of risk sharing and vertical equity

We use concentration curves to measure to which extent premium design will impact the distri-

bution of healthcare payments between low and high healthcare users (risk sharing) and low and

high income groups (vertical equity). We adopt an ex post approach and consider all healthcare

payments, i.e. premium and OOP expenditures. We perform the analysis on the whole popu-

lation, either insured or not (for SHI), to examine the effect of adverse selection on risk sharing

and income transfers when insurance is voluntary. We use concentration curves to represent the

income distribution, the distribution of healthcare costs and the expost distribution of health-

care payments. We compute Gini and Kakwani indexes to measure the impact of healthcare

payments on income distribution (vertical equity). We use similar tools to examine to which

extent healthcare costs are disconnected from healthcare payments (risk sharing). Formulas

and the Stata code used to compute the indexes can be found in the appendix.

3.3.1 Vertical equity

Figure 3.1 presents schematically the concentration curves and the indexes we will use in our

analysis. The North-West diagram represents the Lorenz curve of income. The Gini coeffi-

cient6, GI , gives a measure of income inequalities, ‘at the start’, before healthcare payments.

Concentration curves for payments plot the cumulative proportion of healthcare payments in-

cluding premium and final OOP against the cumulative proportion of the population (ranked

6The Gini coefficient is twice the area between the Lorenz curve and the line of equality

3.3 Measuring the extent of risk sharing and vertical equity 135

according to income, as for the Lorenz curve) (North-East diagram). The diagonal represents

strictly uniform payments. When the curve lies below the diagonal line, the concentration index

for payments7, CI , is positive, meaning that higher income groups bear a bigger share of ex

post healthcare payments (premium + OOP). By comparing the concentration curves for pay-

ments with the Lorenz curve, we can measure whether a payment is progressive or regressive

(South-West diagram). When the concentration curve lies above the Lorenz curve then the

payment scheme is regressive: the lower income groups bear a relatively bigger share of the

health care payments compared to their share in society’s income. The Kakwani index, com-

puted as KI = CI −GI , will then be negative. The more negative is KI , the more regressive the

payments. Finally we can measure the effect of health insurance schemes on income distribution

by comparing the Lorenz curves before and after healthcare payments (South-East diagram).

Let’s define GI−(P +OOP ) as the Gini coefficients after healthcare payments. The redistribution

effect of healthcare payments, REI = GI − GI−(P +OOP ) will be positive if healthcare payments

yield income transfers from the rich to the poor.

3.3.2 Risk sharing

To measure risk sharing, we still use concentration curves and equity indexes but we adapt

them to focus on the extent of transfers between low and high healthcare users (see Figure 3.2).

Instead of using the cumulative population ranked by income in the horizontal axis we rank

the population according to their total annual supplementary healthcare expenditures (SHE),

i.e the amount that individuals would pay if they did not have SHI coverage. The Lorenz curve

becomes a representation of the SHE distribution in the population (North-West diagram). A

high Gini coefficient, GSHE , means that SHE are concentrated at the top of the distribution.

Similarly, the concentration curve of payments plots the cumulative proportion of healthcare

payments, including premium and OOP expenditures (North-East diagram) against the cumula-

tive proportion of the population ranked according to SHE. If the curve lies below the diagonal,

then CR > 0, meaning that high healthcare users contribute more than low users in terms of

healthcare payments. On the contrary, CR < 0 implies that low healthcare users contribute

more than high healthcare users. This can be the case with comprehensive coverage (low OOP)

7The concentration index for payments is twice the area between the concentration curve and the line ofequality

136 Chapter3

and higher premiums for low healthcare users. Note that without insurance, the premium is

null and OOP = SHE, therefore CR = GSHE . A comparison between the concentration curve

and the Lorenz curve assesses whether payments are regressive (South-West diagram). Indeed,

high users might contribute more than low users in absolute terms but still bear a share of

healthcare payments which is lower than their share in society’s SHE. In this case, the Kakwani

index KR = CR − GSHE will be negative. Finally, the overall redistribution between low and

high users is measured as the area between the Lorenz curves with and without insurance, that

is RER = GSHE − GP +OOP .

We argue that measuring the effect of health insurance premiums on vertical equity on the one

hand and risk sharing on the other hand can accommodate different conceptions of fairness.

If vertical equity is the main goal, a fair premium would imply CI > 0 (the rich contribute

more), KI > 0 (payments are progressive) and REI > 0 (there is redistribution from the rich to

the poor) and regimes can be ranked according to these criteria. If society’s goal is to achieve

horizontal equity and maximize risk sharing then a fair premium would imply CR < 0 (low

users contribute more), KR < 0 (high users contribute proportionally less than low users) and

RER > 0 (the distribution of SHE is less unequal after health insurance).

3.4 Decision to take out SHI, premiums and market’s dynamic

Our purpose is to examine the impact of SHI healthcare payments (premiums + OOP) on risk

sharing and vertical equity. We consider 6 regimes of premium, and model for each of them the

decision to subscribe to SHI. When premiums are based on a form of CR, i.e. depend on the

average healthcare expenditure of the pool of subscribers, we use an algorithm to simulate the

consequences of subscription decisions on market size and premium levels.

3.4.1 Health insurance premiums

We consider six regimes of premium: uniform, age-based, medical underwriting, experience

rating, income-based and income/age-based premiums where contributions are based on income

but vary also depending on age groups. There are two different principles among the regimes

3.4 Decision to take out SHI, premiums and market’s dynamic 137

of premium: (i) premiums based on a form of CR, where the level of premium is, to a certain

extent, disconnected from individual risk and based on the average expected expenditures of

the pool of subscribers; (ii) actuarially fair premiums, only based on the individual expected

expenditures and which do not depend on other subscribers’ risk. CR premiums are: uniform,

age-based, income-based and income/age-based premiums. They all imply a form of community

rating: premiums depend on the average SHI reimbursements of the pool P . When insurance is

voluntary, the pool can vary so that the level of CR premiums will be conditional to the pool.

Actuarially fair premiums are: medical underwriting and experience rating. These premiums

depend only on individuals’ characteristics and do not vary with the pool. We assume null

profits: as not-for-profit organizations, mutuelles’s objective is to break-even. A load factor

of 20% is charged by insurers to cover administration costs (the estimated load factors on the

French market ranges from 15% to 25%). For the sake of simplicity, the load factor does not

appear in the equations below. We compute it as an extra 20% on individuals’ premium.

When premiums are uniform, the premium πU is simply the average insurance reimbursements

of the pool: πU = E(SHIR|P ). When insurers are allowed to adjust premium with age,

the premium πa is the average insurance reimbursements for age group a in the pool: πa =

E(SHIR|a,P ).

When premium are income-based, the contribution rate, τ , is the same for all level of income

and satisfies τ = E(SHIR|P )E(y) where E(y) is the average income of the pool. The premium for

individuals with income yi is then πy = τ ∗ yi. To define income/age-based premium we follow

the rule applied by the MGEN: individuals under 30 will face a rate τ1, those between 30 and

60 will face a rate τ2 and those over 60 a rate τ3. An individual with an income yi who belongs

to age group j will pay a premium πincome/age = yi ∗ τj . Appropriate contribution rates must

satisfy:

E(SHIR|P ) = τ1 ∗ E(y1) ∗ δ1 + τ2 ∗ E(y1) ∗ δ2 + τ3 ∗ E(y3) ∗ δ3

with E(yj) the average income of individuals of age group j = 1,2,3 in the pool ; and δj the

proportion of age groups j in the pool. Furthermore, MGEN sets τ2 = 1.25∗τ1 and τ3 = 1.5∗τ1.

Thus,

138 Chapter3

τ1 =E(SHIR|P )

E(y1) ∗ δ1 + 1.25 ∗ E(y1) ∗ δ2 + 1.5 ∗ E(y3) ∗ δ3

The principle of actuarial premiums is that insurers can use individuals’ characteristics to predict

their future SHI reimbursements. We distinguish medical underwriting and experience rating on

the basis of the information used to predict SHI reimbursements. Under medical underwriting,

to compute individual i’s premium for year t, insurers use socio-economics characteristics, Xi,t,

as well as information about previous and current health state, Hi,t, Hi,t−1, Hi,t−28. Under med-

ical underwriting individual i’s premium is therefore πmu = E(SHIR|Xi,t,Hi,t,Hi,t−1,Hi,t−2).

Note that the premium does not depend on the pool. Under experience rating, insurers

can also use previous healthcare consumption, SHEi,t−1, SHEi,t−2 to predict future SHI

reimbursements. Under experience rating, individual i will therefore pay a premium πer =

E(SHIR|Xi,t,Hi,t,Hi,t−1,Hi,t−2,SHEi,t−1,SHEi,t−2). Again, premiums do not depend on the

pool.

3.4.2 Individuals’ decision to take out SHI

Individuals are utility maximizers who share the same utility function u(C), with u′ > 0 and

u′′ < 0. They differ in income level yi, and risk group, λ, which depends on socio-demographic

characteristics, Xi,t, previous and current health status, Hi,t, Hi,t−1, Hi,t−2, as well as past

medical consumption, SHEi,t−1, SHEi,t−2. Each risk group λ is associated with a distribution

of supplementary healthcare expenditures Fλ(SHE), SHI reimbursements Gλ(SHIR) and final

out-of pocket Φλ(OOP ). By definition, OOP is the amount of medical expenditures borne by

patients after health insurance reimbursements (OOP = SHE − SHIR).

Health insurance contracts are available at a premium πi,g,P which can depend on individual

characteristics i, regime g and pool P . Note that in our framework where there is only one

insurer and insurance is voluntary, the pool P is simply the group of individuals who decide to

take out SHI. We suppose that contracts are standardized: there is only one contract available

and the extent of coverage (SHIR/SHE) does not vary with individuals’ characteristics nor

premium design.8We have data over 3 years hence the possibility to use information about the 2 previous years

3.4 Decision to take out SHI, premiums and market’s dynamic 139

Facing a premium πi,g,P , individuals decide to be insured or not. If they decide to be insured,

they pay a premium πi,g,P , face an uncertain realization of SHE and pay out-of-pocket expen-

ditures OOP . If they decide to be uninsured, they do not pay a premium but will bear the

whole risk of their future supplementary healthcare expenditures SHE.

Because individuals are utility maximizers, they buy health insurance if their expected utility

when being insured is higher than when uninsured. Formally, we can define expected utility

when uninsured as:

EUuninsuredyi,λ =

∫ +∞

0u(yi − SHE)dFλ(SHE) (3.1)

Similarly we define expected utility when insured as:

EU insuredyi,λ,g,P =

∫ +∞

0u(yi − πi,g,P − OOP )dΦλ(OOP ) (3.2)

Therefore, under regime g and considering the pool P , individual i buys health insurance if

EU insured > EUuninsured and remains uninsured otherwise.

A key assumption of our model is that Fλ(SHE) is assumed to be the same whether indi-

viduals are insured or not. Indeed, we are not able to estimate a counterfactual distribution

when individuals do not subscribe to SHI. In other words, we have to assume that individu-

als’ healthcare expenditures are orthogonal to insurance coverage. This is a strong assumption

considering, on the one hand, evidence on foregone healthcare for individuals without SHI in

France (Buchmueller & Couffinhal 2004) and, on the other hand, evidence of moral hazard for

those who benefit from comprehensive SHI coverage (Dormont & Péron 2016). We discuss the

implications of this assumption on our results in section 3.6.5.

3.4.3 Market’s dynamic when insurance is voluntary

When insurance is mandatory, individuals have no choice but to be insured and the pool remains

always the same. When insurance is voluntary and when premiums are based on a form of

community rating, their level depend on the expected SHE of individuals who took out SHI

140 Chapter3

(the pool P ). Hence, we must simulate individuals and insurer interactions on what we call the

SHI market. Formally, when considering the dynamic at stake, the decision to take out SHI can

be described as follows:

Step 1: individuals compute their expected utility without insurance EUuninsuredyi,λ

=∫

u(yi −

SHE)dFλ(SHE). This depends on individuals’ characteristics only and will not be affected by

pool composition.

Step 2: P0, the initial pool, is supposed to include the whole population. We suppose that the

insurer sets premiums conditional on regime g assuming that all individuals want to be insured.

In each subsequent iteration j, the insurer computes the premium level πi,g,Pjlinked to the new

composition of the pool Pj .

Step 3: individuals compute their expected utility with insurance EU insured =∫

u(yi − πi,g,P −

OOP )dΦλ(OOP ) under regime g and pool P = Pj−1. If EU insured > EUuninsured they buy

insurance and stay in the pool Pj . Otherwise, they exit the pool and become uninsured.

We repeat Steps 2 and 3 for j = 1 to n until we reach an equilibrium, i.e. until Pj equals Pj−1

and pi,j = pi,j−1. In reality, the iteration can result from anticipation by insurers of the market’s

dynamic or from an adaptive process, with insurers adjusting year after year their premiums to

the pool. Note that there are two cases with no such dynamic: mandatory SHI and premiums

set on individual risk only (actuarial fairness).

3.5 Empirical application

In this section, we present the database used for the simulations and descriptive statistics on the

distribution of SHE, SHIR and OOP payments in our sample. We use these data to estimate

individuals’ risk, compute health insurance premiums for each regime g, expected utilities,

decision to subscribe to SHI and final outcomes in terms of healthcare payments.

3.5 Empirical application 141

3.5.1 Data

We use a data set from a French supplementary health insurer, Mutuelle Générale de l’Education

Nationale (MGEN). MGEN is a not-for profit insurer which mainly insures teachers and minis-

ter of education employees, active or retired. MGEN processes claims on behalf of mandatory

NHI and also provides a voluntary SHI (MGEN-SHI): a unique contract that covers co-payments

as well as medical goods and services not covered by the NHI9. The MGEN-SHI benefits are

representative of the average coverage offered by other SHI contracts in the individual market in

France: balance billing is not covered and optical and dental care coverage is limited (DREES

2016). We have at our disposal a sample of 87,110 individuals, aged between 25 and 90 and

observed from 2010 to 2012. During this period, they are all covered by MGEN-SHI contract

and consequently all benefit from the same coverage. Using MGEN’s administrative data, we

are able to identify, annually and for each individual, (i) supplementary healthcare expendi-

tures not covered by mandatory public insurance (SHE) ; (ii) supplementary health insurance

reimbursements (SHIR) ; (iii) final out-of-pocket payments (OOP ). We also have information

about socio-economic characteristics such as age and gender as well as whether individuals suffer

from a chronic disease or the number of days they spent in hospital during the year. Because

MGEN premiums are based on income we are also able to reconstruct individuals’ income.10

3.5.2 Descriptive statistics

Table 3.1 summarizes the main socio-demographic characteristics of our sample. We confront

these figures with the characteristics from the ESPS sample11 deemed representative of the

French population. Because MGEN-SHI covers mainly minister of education employees, women

are over-represented. It is also possible that the MGEN sample is already adversely selected due

to income-based premium. This is especially true for the youngest age group which seems to be

under-represented in the MGEN pool compared to the whole population. However in terms of

health condition, the percentage of individuals with a chronic disease among the MGEN pool

9Like most of the SHI contracts in France, the MGEN-SHI contract is a Contrat solidaire et responsable10This proxy is actually close from a truncated wage. Indeed, there is a minimum premium for monthly income

under e1000 and a ceiling for income above e4900. Also, premiums are only based on wages or pensions andtherefore do not take into account other sources of income.

11Enquête Santé et Protection Sociale (ESPS) is a bi-annual survey conducted on a sample of 8,000 Frenchhouseholds, i.e. 22,000 individuals representative at 97% of French population

142 Chapter3

is very similar to the one reported by the ESPS survey.

Table 3.2 presents the empirical distribution of supplementary healthcare expenditures, SHI

reimbursements and OOP payments from the MGEN sample in 2012. Because we focus on

healthcare expenditures financed through SHI, the part reimbursed by NHI does not appear

here. This explains why the average SHE per individual does not exceed e716 per year. How-

ever, the SHE distribution is highly skewed and SHE may amount to more than e16,000 per

year. Furthermore, OOP payments are not capped in France and can reach e13,960 as observed

in our sample. As a result, average figures on SHE or OOP payments do not say much about the

risk actually faced by individuals and underestimate the role of SHI in the coverage of healthcare

expenditures. We must therefore consider the whole distribution of SHE and especially look at

the top users. Figure 3.3 presents the Lorenz curves and associated Gini coefficients of SHE

(North-West diagram), SHI reimbursements (North-East diagram) and OOP payments (South-

West diagram) from our MGEN sample in 2012. It is worth noting that the high concentration

of total healthcare expenditures on the top users, well documented in France for the mandatory

scheme (HCAAM 2013), is also valid for SHE in France. The last two deciles of our sample

are responsible for 60% of the total SHE and the Gini coefficient, GSHE , amounts to 0.54. The

Lorenz curve for reimbursements (SHIR) presents roughly the same shape (GSHIR = 0.52).

OOP payments are more concentrated with a Gini coefficient of 0.66. Indeed, the last two

deciles bear almost 70% of the total OOP expenditures.

As regards income distribution (Figure 3.4), our sample presents a Gini coefficient, GI , of 0.18.

By comparison, the Gini coefficient for the whole French population was 0.30 in 2012 (Houdré

et al. 2014). Obviously, because most of MGEN-SHI enrollees are teachers, the MGEN popu-

lation is more homogeneous in terms of wages than the whole population12. Moreover, for our

sample, healthcare utilization seems relatively orthogonal to income. Indeed, the concentration

curves for SHIR and OOP are very close to the diagonal: concentration indexes for SHIR (-0.03)

and OOP (0.004) slightly depart from zero. Note that the absence of a clear correlation between

healthcare expenditures and income is not specific to our sample. Using a sample representa-

tive of the French population, Duval et al. (2012) do not give evidence of sizeable differences in

healthcare expenditures across income deciles.12Moreover, there is a truncation on top and bottom of the distribution of our income proxy

3.5 Empirical application 143

Finally, we come back to our main concern about age-based premiums by focusing on the

first, fifth, ninety-fifth and ninety-ninth percentiles as well as the mean of SHI reimbursements

by age, from 25 to 90 years old. Figure 3.5 shows that the mean and the variance of SHI

reimbursements continuously increase with age, almost linearly. However, age only explains

6.5% of SHIR variability (Table 3.3). This makes age a quite convenient, yet not very precise,

predictor of supplementary healthcare expenditures and confirm that age-based premiums are

in between community rating and actuarial fairness.

3.5.3 Calibration and computation

We estimate individuals’ own appreciation of risk, λ, by regressing SHE on socio-demographic

characteristics such as gender, age and income. We also control for chronic disease and hospital

stays that occurred within the last two years as well as their SHE for the two previous years such

that SHEi,2012 = E(SHE|Xi,2012, Hi,2010−2012, SHEi,2010−2011) (Table 3.4). We then use the

prediction of SHE to build four groups λj with j = 1,2,3,4. The four groups correspond to the

four quartiles of predicted SHE. Considering risk groups rather than directly the individual’s

expected SHE allows us to consider a whole distribution of SHE rather than an average expected

value. Indeed, even though the individual is able, based on her characteristics and experience,

to estimate her expected SHE, she still faces the risk that her actual SHI will be higher or lower.

Despite the use of a rather simple predictive model, our four groups are very distinct in terms

of ex post empirical average expenditures, from e333 for the lower risk group to e1215 for

the highest; the variance also increases with λ. Besides, OOP payments also vary significantly

between groups (Tables 3.5 and 3.6). We estimate for each group λ the empirical distribution

of SHE, Fλ(SHE), and OOP payments, Φλ(OOP ), with a kernel function. Figure 3.6 displays

the empirical distribution function of SHE for each risk group and shows the sizeable differences

between groups. The empirical distributions of SHE and OOP conditional on risk groups λ

are used to compute the values of expected utility respectively with and without insurance, as

defined in equations (3.1) and (3.2).

The insurer perspective is different from the individual’s own risk appreciation. First, the

insurer focuses on SHI reimbursements rather than SHE. Indeed, OOP payments, by def-

inition the expenditures not covered by SHI, do not directly intervene in premiums calcu-

144 Chapter3

lation. Second, the predicted SHIR is sufficient to compute individual’s premium because

among the pool, the sum of premiums will eventually equal the pool’s SHIR. The explana-

tory variables used in the insurer’s predictive model will depend on the way premiums are

defined. Under medical underwriting, the insurer can use socio-demographic characteristics

and information about health state recorded by a questionnaire filled at subscription (chronic

disease, hospital stays): SHIRi,2012 = E(SHIR|Xi,2012, Hi,2010−2012). Because insurers can-

not adjust the premium on previous consumption, individuals still benefit from private in-

formation. Under experience rating though, where previous SHE are used to predict indi-

vidual’s future SHIR, information is symmetric between insurers and individuals such that

SHIRi,2012 = E(SHIR|Xi,2012, Hi,2010−2012, SHEi,2010−2011).

To compute expected utilities of equations (3.1) and (3.2), we assume that the individual uses

a von Neumann Morgenstern utility function of the form:

u(C) = −1γ

∗ e−γC , (3.3)

where γ is the constant absolute risk aversion (CARA) parameter. We are here in line with the

choice made by several papers when estimating risk aversion (see Einav et al. (2013)) or Handel

et al. (2015))13. Unfortunately, our data do not allow us to estimate an individual risk aversion

parameter. So we consider that risk aversion is homogenous across our population and set

γ = 0.0005 (Handel et al. (2015) estimated a mean CARA parameter equals to 0.00044 on US

data), with robustness checks for values lying between 0.0004 and 0.0006.

Finally, we use a VBA macro (the code is available in the appendix) to compute premiums and

compare for each individual, her expected utility with and without insurance, taking into ac-

count market’s dynamic thanks to a loop. Whatever the regime, there is always some individuals

who want to subscribe to SHI and an equilibrium is reached after less than 11 iterations.

13As regards health insurance, the question of a decreasing, constant or increasing aversion with incomeis an interesting one. Dormont et al. (2009)) analyze coverage choices in Switzerland and find that demandfor basic insurance coverage decreases with income, suggesting a decreasing absolute risk aversion. However,demand for supplementary coverage increases with income. They explain this apparent paradox by the fact thatsupplementary insurance gives access to ‘luxury’ medical goods and so willingness to pay for these goods mightwell increase with income. In our case, French supplementary insurers actually cover both basic and supplementalmedical goods. Assuming a CARA would then cancel out the two expected effects of income as regards demandfor coverage.

3.6 Results 145

3.6 Results

Our results are displayed in Tables 3.7 to 3.11. They stem from the simulations performed on

the MGEN sample assuming a risk aversion parameter equal to 0.0005 and a load factor equal

to 1.2. We first focus on the impact of voluntary SHI on insurance coverage and premiums

paid. We then analyze the impact of age-based premiums on vertical equity and on risk sharing

relative to other regimes of premiums, from pure CR to actuarial fairness. We finally provide

robustness checks.

3.6.1 Consequences of voluntary SHI

Table 3.7 summarizes, for each regime of premium (uniform, age-based, medical underwriting,

experience rating, income-based and income/age-based), the simulated average premium for

the whole sample and for groups of interest when SHI is either mandatory or voluntary. The

most important gap between age groups results from age-based premiums when insurance is

voluntary with a ratio of 2.38 between the youngest (e311 for the 25-35 years old) and the oldest

group (e742 for those over 65). With age-based premiums, the poor also contribute more than

the rich: their premium is on average 12% higher. The premium ratio between low risks (λ1)

and high risks (λ4) amounts to 1.88 and is significantly higher than for uniform premiums (1

by definition) or income-based premiums which show a ratio lower to 1 (0.93) because of the

negative correlation between SHI reimbursements and income. On the contrary, the premium

ratio between low and high risk groups is just slightly lower for age-based premiums than for

medical underwriting (1.88 vs 2.13). Unsurprisingly, experience rating yields the biggest gap

between high and low risks with a ratio of 2.86.

Because age is a predictor of SHI reimbursements, age-based premiums tend to share more com-

mon features with actuarial premiums than uniform or income-based premiums. The similarity

between age-based and actuarial premiums implies that age-based premiums are less affected

by the absence of a mandate on SHI, contrary to uniform and income-based premiums. Indeed,

when insurance is voluntary, the average age-based premium increases by 5.7% whereas uniform

premiums increase by 36% and income-based premiums by 52%. As a matter of fact, 50.6% of

146 Chapter3

our sample decide not to be insured when premiums are income-based and insurance is volun-

tary. As shown in Table 3.8, these leavers are mostly young and healthy individuals. Setting

different contribution rates by income and age does not significantly limit the loss of insured

(47.4%) and the average premium still increases by 40.5%. On the contrary, when premiums

are based on the individual risk, non-insurance rates are much lower. Interestingly, medical

underwriting presents roughly the same non-insurance rate than age-based premiums. This is

explained by the proximity of the two regimes. Even though medical underwriting allows the

insurer to use more variables to predict SHI reimbursements (gender, chronic disease, hospital

stays), age is the main driver of SHIR. If we predict SHIR first based only on age groups and then

add the other variables, the correlation between the two predicted values equals 0.89. When

adding previous consumption of healthcare (as under experience rating), the correlation drops

to 0.67. Experience rating is indeed closer to individuals risk and the proportion of uninsured

is consequently very low (3.6%).

Who give up SHI? Table 3.9 displays the percentage of uninsured by income and risk profile for

each regime. It shows primarily that healthy individuals, with a rather low expected SHE (λ1,

λ2), are more likely to be uninsured. This is especially true when premiums are disconnected

from individual risk (uniform or income-based premiums). As stated previously, this adverse

selection phenomenon has important consequences on the extent of risk sharing. First, premiums

will increase for those who remain in the pool: CR premiums depend on the average expenditures

of the pool which is now made of high healthcare users. Because of increasing premiums, the

disconnection between healthcare payments (premiums + OOP) and healthcare expenditures

(SHE) is lower for high healthcare users. Second, among those who are uninsured, risk sharing

will be null by definition. Hence, we can expect an important reduction of risk sharing when

insurance is voluntary and premiums based on CR. When premiums increase with risk (age-

based premiums, medical underwriting and experience rating), low income individuals with high

expected SHE are more likely to give up SHI than higher income groups. In a sense, considering

their tight budget constraint, they prefer the uncertainty of high OOP payments rather than

the certain payment of a high premium.

3.6 Results 147

3.6.2 Age-based premiums and vertical equity

Table 3.10 displays the indexes previously defined in section 2 which measure the extent of

vertical equity resulting from healthcare payments (premium and OOP payments). GI is the

Gini coefficient of income distribution before healthcare payments; GI−(P +OOP ) is the Gini

coefficient of the income distribution, after healthcare payments; CI is the concentration index

of healthcare payments relative to income distribution; KI is the Kakwani index relative to

income distribution; and finally REI is the income redistribution index. We report the index

values for each of the six different regimes (uniform, age-based, medical underwriting, experience

rating, income-based and income/age-based) when insurance is either mandatory or voluntary.

We also report the index values in a situation without insurance. In order to make comparisons

between the distinct regimes easier, Figure 3.7 displays for each regime, the concentration index,

the Kakwani index and the redistribution index when insurance is mandatory or voluntary.

Vertical equity would imply a positive concentration index, CI and a positive Kakwani index

KI : high income groups would contribute more than low income groups and more than their

share in society’s income. The higher REI , the larger the income redistribution.

As regards progressive payments and income redistribution, age-based premiums perform poorly:

– When insurance is mandatory, age-based premiums are more regressive than uniform premi-

ums (KI = −0.1933 vs KI = −0.174) and are even worse than a situation without insurance in

terms of income redistribution (REI = −0.0057 vs REI = −0.0055). On the contrary, financing

healthcare through income-based contributions achieves vertical equity: health care payments

are still regressive due to OOP payments (KI = −0.06) but the redistribution index is higher

than for any other regime (REI = −0.002).

– When insurance is voluntary, because of a large number of uninsured when premiums are

based on income, income distribution on the whole population is dramatically reduced: the

redistribution index drops from -0.002 to -0.0043. By comparison, the redistribution index

when premiums are based on age equals -0.0055. Although the percentage of insured is slightly

higher when income-based premiums also depend on age, the effect on income redistribution is

not really improved (REI = −0.0043).

148 Chapter3

3.6.3 Age-based premiums and risk sharing

Table 3.11 displays the indexes that measure the effect of each regime of premiums on risk

sharing, when insurance is either mandatory or voluntary. GSHE is the Gini coefficient for

the SHE distribution; GP +OOP is the Gini coefficient for the healthcare payments distribution;

CR is the concentration index of healthcare payments relative to SHE distribution; KR is the

Kakwani index relative to SHE distribution; and finally RER is the ‘risk redistribution’ index.

Figure 3.8 displays the concentration index, the Kakwani index and the redistribution index

when insurance is mandatory and voluntary. Of course, in any case, uninsured individuals are

included in the computation of indexes. For interpretation, remember that a positive concen-

tration index CR implies that high users contribute more to payments than low users. There

is risk sharing when the Kakwani index, KR, is negative. In this case, the share of high users

in payments is lower than their share in medical expenses (SHE). Finally, the higher RER, the

higher the extent of risk sharing.

– Without insurance, the distribution of healthcare payments is similar to the distribution of

SHE. The redistribution index equals zero. By contrast, if insurance were mandatory with

complete coverage, uniform premiums would guarantee the highest level of risk sharing. No

matter how unequal the distribution of SHE can be, uniform premiums would take the Gini

coefficient back to zero. When coverage is partial however, the unequal distribution of OOP

payments limits the effect of uniform premiums on risk sharing. Indeed, based on our sample,

the Gini coefficient for the SHE distribution (GSHE = 0.5435) is only reduced by 0.3131 points

after insurance.

– When insurance is mandatory, age-based premiums are in between pure CR and actuarial

premiums in terms of risk sharing. With a redistribution index of 0.2509, premiums adjusted

on age limit the extent of redistribution between low and high users compared to uniform

premium (RER = 0.3131) or even income-based premiums (RER = 0.2690) but still perform

better than medical underwriting (0.2393) and experience rating (0.2095). These results give

evidence of a continuum of premiums in terms of risk sharing from pure CR to actuarial fairness,

and at the extreme limit no insurance. Age-based premiums are situated in between.

3.6 Results 149

– When insurance is voluntary, the effect of premiums on risk sharing dramatically changes and

the opposition between CR and actuarial fairness is no longer valid. Uniform and income-based

premiums particularly suffer from adverse-selection. A large fraction of the population prefers

to exit the pool and consequently premiums increase for those who remain insured. In the case

of uniform premiums, 50.5% of our sample leave insurance and the redistribution index conse-

quently drops from 0.3131 to 0.1238. The loss is more dramatic for the income-based regime

which shows the lowest redistribution index (RER = 0.1019). One important result is that

actuarial premiums (medical underwriting or experience rating) allow higher risk sharing than

uniform and income-based premiums when insurance is voluntary, with respectively redistribu-

tion indexes equal to 0.2014 and 0.2024. Indeed, even if premiums are closer to the individual

risk, the high proportion of insured guarantees a higher level or risk sharing than CR. This

effect is reinforced by the fact that there is a large uncertainty regarding the ex post realization

of required reimbursements (SHIR). Indeed, between 86 to 92% of SHIR variance is unexplained

by individual characteristics and previous healthcare expenditures (Table 3.4). Similarly, age-

based premiums resist to adverse selection and still allow community rating within age groups,

hence achieving the largest risk sharing when insurance is voluntary (RER = 0.2096).

3.6.4 Robustness checks

Large OOP payments necessarily limit risk sharing: by definition, healthcare expenditures which

are not covered by insurance cannot be socialized. In France, OOP payments after SHI have

two elements: NHI co-payments that cannot be covered by SHI (e1 deductible per consultation

for instance) and other goods only partially covered by SHI (balance billing, optical or dental

care). It is difficult to draw clear conclusions about the impact of OOP payments on vertical

equity, because OOP payments are directly related to healthcare use. Indeed, if OOP concerns

normal goods or services for which demand increases with income, then the rich are likely to

have higher OOP expenditures than the poor. In this case, payments would be progressive.

However, because progressivity comes from the demand behavior of high-income individuals,

it is hard to consider it as a fair situation. To examine whether our conclusions might be

changed, we run the same analysis but limit the scope to expenditures that are covered by SHI.

Table 3.12 shows that our conclusions do not change: when insurance is voluntary, risk sharing

150 Chapter3

is maximized with age-based premiums, still however at the expense of vertical equity.

Our results on vertical equity and risk sharing are very sensitive to the percentage of the

population that chooses to remain uninsured. As we demonstrated previously, the way to

define premiums plays an important role. However, two parameters are also likely to drive the

results: the load factor and the risk aversion parameters. Our main simulation is based on a

load factor of 1.2 and a risk aversion parameter of 0.0005. Table 3.13 provides the simulation

results, when insurance is voluntary, for different values of the load factor (1.1 and 1.15) and

of the risk aversion parameter, γ in equation 3.3 (0.0004 and 0.0006). A lower load factor

reduces the price of insurance and is likely to encourage individuals to take out insurance.

We are able to verify that a load factor of 1.1 rather than 1.2 as in our base-case slightly

decreases the proportion of uninsured, especially for uniform premiums. However, age-based

premiums still yield higher risk sharing than uniform or income-based premiums. Surprisingly,

medical underwriting performs even better than age-based premiums. With a load factor of 1.15

results are unchanged compared to the base-case scenario. When individuals are less risk averse

(0.0004 instead of 0.0005), the percentage of uninsured dramatically increases, even for age-

based premiums. As regards vertical equity, income-based premiums, despite a large number

of uninsured, still yield less regressive healthcare payments than other forms of premiums.

However, when risk aversion is higher than in our base-case scenario (0.0006 instead of 0.0005),

results are unchanged.

3.6.5 Discussion

Do the mutuelles deny their founding solidarity principles when using age-based premiums?

Our simulations show that when insurance is voluntary, age-based premiums allow the largest

transfers from low to high healthcare users. Indeed, age-based premiums are a cross-breed

between CR and actuarial fairness: they better resist to adverse selection than uniform or

income-based premiums and still guarantee more risk sharing than actuarially fair premiums.

Remarkably however, age-based premiums are very close to medical underwriting in terms of

level of premiums, profile of uninsured and impact on risk sharing and vertical equity. Indeed,

even when using information on gender, chronic disease or hospital stay, age remains the main

driver of SHI reimbursements. This is interesting because medical underwriting is strongly

3.6 Results 151

discouraged in the French SHI market based on the idea that it is not fair. We show that

premiums increasing with age are not very different in practice. At least as long as NHI covers

a major part of inpatient care and do not charge co-pays for care related to chronic disease. To

sum up, in a context of voluntary SHI, age-based premiums are best to preserve risk-sharing;

but what about vertical equity?

When insurance is voluntary, there is a conflict between the objective to disconnect healthcare

expenditures from healthcare payments and to guarantee vertical equity. It is especially true

when comparing age-based and income-based premiums. On the one hand, age-based premiums

maximize risk sharing but yield more regressive payments than income-based premiums. On the

other hand, income-based premiums is the least regressive type of payments but also encourage

healthy individual to be uninsured, which dramatically limits the extent of risk sharing. Should

we give priority to risk sharing or vertical equity? According to the Welfarist literature, the key

argument to use health insurance for income redistribution is that the correlation between risk

and income has to be negative. However, in line with the results from Duval et al. (2012) on

general population, we do not find in our data a strong correlation between SHE and income.

Note that this conflict between risk sharing and vertical equity is less striking when insurance

is mandatory. In this case, income-based premiums are superior to age-based premiums both

in terms of risk-sharing and vertical equity. This is related to another important result of our

simulations: a voluntary insurance dramatically limits the extent of solidarity. In this respect,

the negative impact of adverse selection on SHI coverage and level of premiums is not different

from what the literature has reported for basic health insurance. Analyzing the introduction

of a mandate in Massachussetts’ individual health insurance market, Hackmann et al. (2015)

report a growth in coverage associated with a significant reduction in the level of premium.

They estimate an increase in welfare of 4.1% due to reduction in adverse selection alone. Our

simulations show that we could expect the same outcomes in the context of SHI.

Our simulations illustrate how age-based premiums impact the distribution of healthcare pay-

ments taking into account correlations between age, risk and income in the context of SHI.

They also emphasize adverse selection phenomenons and reveal the conflict between risk shar-

ing and vertical equity when insurance is voluntary. However, our results have to be interpreted

152 Chapter3

carefully considering the assumptions we make in our model and the inherent limits of equity

indexes. We believe there is also room for improvement and propose possible extensions to this

work.

When modeling individuals’ decision to take out SHI, we rely on several assumptions. Especially,

we do not take into account costs related to the decision to be uninsured such as switching costs

or individuals’ anticipation that their premium might increase if they subscribe to SHI too late.

The percentage of uninsured for CR premiums resulting from our simulations might therefore be

overestimated, compared to reality. For instance our model predicts than 47.4% of our sample

would give up SHI if premiums were based on income and age. Yet, our sample is precisely made

of MGEN-SHI enrollees who, despite income-based premiums, still subscribe to SHI. There are

several reasons that can explain this apparent drawback. First, we do not take into account

inertia. Studies on switching behavior in health insurance show that individuals tend to remain

with the same insurance contract even if they would benefit from switching (Strombom et al.

2002, Marzilli Ericson 2014, Handel 2013). Second, because MGEN also processes NHI claims,

enrollees can find easier to subscribe to MGEN-SHI. Finally, the MGEN-SHI includes benefits

beyond healthcare such as invalidity and dependance insurance that can attract enrollees. The

switching rate in MGEN-SHI is indeed relatively low (about 1.5% per year). However, they have

difficulties to recruit new enrollees, especially among young teachers. We are more confident

as regards the simulated proportion of uninsured for age-based premiums which equals 10%.

Indeed, the proportion of individuals without SHI is about 6% in France, including private

sector employees for which SHI is subsidized. The proportion of uninsured varies between 6 and

15% for unemployed, inactive and retirees, likely to buy SHI on the individual market where

premiums are based on age (Perronnin et al. 2011).

Taking into account the articulation between NHI and SHI will be an important extension

to this work. There are two questions we want to investigate: (i) Does SHI cancel out the

solidarity implied by the NHI?; (ii) What would be the distributional impact of a change in

NHI benefit package? The first question has been pointed out by Bozio & Dormont (2016).

The authors emphasize the contradictory principles between NHI and SHI premiums, especially

in terms of transfers between age group. It would be interesting to quantify to which extent

3.6 Results 153

SHI premiums cancel out NHI transfers between income groups and age groups. The second

question is related to the definition of the NHI benefit package, in its three dimensions (co-pays,

list of medical services included, population). Mechanically, NHI benefits have a direct impact

on SHE magnitude and variance. A change in NHI benefits will also change the correlations

between age, health state and SHI, and therefore the impact of age-based premiums on risk

sharing and on vertical equity.

Also, it is critical to consider issues around SHI affordability, i.e. situations where low income

have to give up SHI because premiums are too expensive. However, concentration curves might

not be the most appropriate tools for investigating this question. We show that when premiums

increase with risk, low income individuals with high expected SHE are more likely to give up

SHI than higher income groups. In terms of fairness, this situation is not desirable. Do vertical

equity indexes reflect the loss of low income and high risk individuals? Not necessarily. It will

depend on the realization of SHE. On the one hand, among low income-high risk individuals,

the ‘lucky’ who have low realized expenditures contribute less than if insurance were mandatory.

On the other hand, the ‘unlucky’ will bear important healthcare payments. Therefore, the effect

on the overall progressivity of healthcare payments is unclear.

Another challenge comes from the ability to take into account the price elasticity of demand

for healthcare. Remember that we assume that being uninsured will not modify individuals’

healthcare consumption. The impact of this assumption on our results is not straightforward.

First, note that assuming a negative price elasticity does not give insights on whether a reduction

in SHE when individuals are not insured is desirable (less moral hazard) or not (foregone

healthcare). Furthermore, even if we were able to estimate SHE distribution without insurance

and to agree that a reduction in SHE is not desirable, the results on vertical equity might be

fallacious. Indeed, imagine a situation where, on the one hand, low income individuals cannot

afford SHI and have to give up on care (resulting in low healthcare payments); and on the other

hand, wealthy individuals pay health insurance premiums and consume important quantity of

care (resulting in large healthcare payments). In this case, payments will be ‘progressive’ despite

an obvious problem in terms of access to SHI and care.

Our difficulties to take into account questions about SHI affordability and access to care are

154 Chapter3

more generally due to our pragmatic definition of fairness. The narrow spectra of income and

healthcare payments, without considering health or healthcare use, might be too limited to

assess the impact of health insurance and premiums on well-being. Fleurbaey & Schokkaert

(2011) state that equity in financing healthcare should be integrated within a broader concept

of well-being, "including provision (of health and health care) and net material consumption

as two relevant dimensions". In this framework, the adverse effect of expensive premiums, not

affordable for low income individuals, would be captured through the negative effect of foregone

care on health. This approach is more satisfying but also more demanding in terms of data.

Indeed, it requires comprehensive information on individuals’ income, health, healthcare use

and healthcare payments.

3.7 Conclusion

In the French SHI market, the mutuelles, not-for-profit insurers, are keeping away from their

founding solidarity principles. To avoid the adverse selection death spiral, they give up on

uniform premiums and set premiums increasing with age. Age-based premiums raise concerns

about inequalities both in the level of premiums and in the extent of coverage. Fairness issues

are also a political argument. It is especially critical for mutuelles who have to convince their

stakeholders that moving towards premiums adjusted on individual’s risk will not go too far

against their founding principles in terms of risk sharing and access to insurance.

Because the theoretical and empirical literature usually considers the NHI level, it is interesting

to take into account the specificity of SHI in terms of correlations between age, income and

healthcare expenditures to illustrate adverse selection phenomenons and the distributional im-

pact of SHI premiums. Furthermore, due to a lack of data, we have seldom knowledge about the

distribution of healthcare expenditures effectively covered by SHI and their impact on income

distribution.

We exploit an original database of 87,110 individuals, aged from 25 to 90 years-old, for whom

we observe their SHI reimbursements and final OOP. We adopt an empirical approach and

use simulation methods to compare the impact of age-based premiums with other regimes

3.7 Conclusion 155

and illustrate adverse selection phenomena in a context of voluntary SHI. We focus on ex post

outcomes to fully take into account the specificity of SHI in terms of distribution of expenditures

and correlations with age, income and health status. We use concentration curves and inequality

indexes to measure the impact of premiums on income distribution and on transfers between

low and high healthcare users.

Based on our simulations, we derive three results on the impact of age-based premiums in the

SHI market. First, in a context of voluntary SHI, age-based premiums is the best solution to

preserve risk sharing. A regime with age-based premiums better resists to adverse selection

than uniform or income-based premiums and still guarantee more risk sharing than actuarially

fair premiums. An interesting result is that, due to the absence of strong correlation between

SHI reimbursements and other individual characteristics than age (gender, chronic disease or

hospital stays), age-based premiums are not very different from medical underwriting. Yet,

medical underwriting is strongly discouraged in the SHI market because it is seen as a very

unfair practice. We show that age-based premiums are not very different, at least considering

the current SHI perimeter. Second, simulations show that age-based premiums achieve risk

sharing at the expense of vertical equity. Indeed a regime with income-based premiums, even if

it suffers from adverse selection yields less regressive payments than age-based premiums. This

conflict between risk sharing and vertical equity is barely discussed in the literature or in policy

debates. Yet, it is striking when insurance is voluntary and deserves more attention. Finally,

we illustrate in the context of SHI a common result in the literature: the absence of a mandate

limits the impact of SHI on risk sharing and vertical equity, especially when premiums are based

on a form of community rating.

Our results enable us to deal with important policy questions as regards the regulation of health

insurance and the way to define premiums. First, we stress out the importance of a mandate

in SHI to avoid adverse selection mechanisms and ensure that healthcare payments are discon-

nected from healthcare expenditures and are ‘fairly’ distributed among income groups. The

political position of the mutuelles in France, whom firmly reject the idea of a mandatory SHI

while pursuing an ideal of community rating, seems therefore difficult to hold. Furthermore,

this result should support the decision to impose a mandate on health insurance, despite the

156 Chapter3

apparent political difficulty to do it. As regards SHI in France, coverage has been mandatory for

private sector employees since January 2016, but still remains voluntary on the individual mar-

ket. This is likely to enlarge the gap between ‘insiders’ (employees) – usually benefitting from

mandatory, subsidized and comprehensive coverage with uniform or income-based premiums

– and ‘outsiders’ (unemployed, self-employed and pensioners) who have to purchase coverage

in the individual health insurance market and face the consequences of adverse selection, i.e.

increasing premiums and limited risk sharing. Second, we show that in a context of volun-

tary insurance, age-based premiums limit the effect of adverse selection and still allow for risk

sharing. This would support mutuelles’ strategy to use age-based premiums. However, our sim-

ulations also point out that age-based premiums yield regressive payments and do not answer

the question of insurance affordability and income inequalities due to healthcare payments.


Tables and Figures

Figure 3.1 – Income, healthcare payments and vertical equity

158 Chapter3

Figure 3.2 – Supplementary healthcare expenditures, payments and risk sharing


Table 3.1 – Socio-demographic characteristics - MGEN sample, 2012

MGEN ESPSN % %

Women 56,887 65.3 51.65Men 30,223 34.7 48.35

25-35 6,609 7.6 16.635-45 14,729 16.9 19.545-55 15,785 18.1 23.055-65 20,080 23.1 20.465-75 18,745 21.5 11.975-90 11,162 12.8 8.7

Low income 18,476 21.2 NAAverage income 47,768 54.8 NAHigh income 20,866 24.0 NA

No chronic disease 70,031 80.4 80.5Chronic disease 17,079 19.6 19.5

No hospital stay 73,460 84.4 NAHospital stay in 2010 only 5,688 6.5 NAHospital stay in 2011 only 5,931 6.8 NAHospital stay in 2010 and 2011 2,031 2.3 NALow income: up to e2000 monthly wage

Average income: between e2000 and e3000

High income: above e3000

160 Chapter3

Table 3.2 – Empirical mean, standard deviation and percentiles of supplementary healthcareexpenditures (SHE), SHI reimbursements (SHIR) and out-of-pocket payments(OOP ), in e,MGEN sample in 2012

N Mean s.d min p1 p5 p50 p95 p99 max

SHE 87,110 716.6 921.4 0 0 27.5 448 2243 4675 16681

SHIR 87,110 436.1 512.1 0 0 15 293 1343 2513 16370

OOP 87,110 281.2 533.1 0 0 3 117 1050 2550 13960


Figure 3.3 – Distribution of supplementary healthcare expenditures (SHE), SHI reimburse-ments (SHIR) and out-of-pocket payments(OOP ), MGEN sample 2012

162 Chapter3

Figure 3.4 – Distribution of income and concentration curves for supplementary healthcareexpenditures (SHE), SHI reimbursements (SHIR) and out-of-pocket payments (OOP ), MGENsample 2012


Figure 3.5 – Distribution of SHI reimbursements by age, MGEN sample 2012

Table 3.3 – Correlation between SHI reimbursements (SHIR) and age

OLS SHIR

Age 6.91*** (0.80)

Age2 0.016** (0.007)

R2 0.0648N 87,110* p<0.1, ** p<0.05, *** p<0.01

164 Chapter3

Table 3.4 – Predicted supplementary health care expenditures (SHE) and SHI reimbursements(SHIR)

Individual’s risk Medical underwriting Experience rating

OLS SHE SHIR SHIR

Intercept 180.4*** 184.6*** 141.2***

Women 111.1*** 66.1*** 37.0***

25-35 ref. ref.35-45 21.2* 33.0*** 26.2***45-55 140.9*** 136.7*** 103.5***55-65 231.7*** 211.9*** 150.7***65-75 343.3*** 292.1*** 208.0***75-90 441.1*** 368.9*** 257.5***

Low income -14.1*** -27.5*** -16.0***Average income ref. refHigh income 42.2*** -2.75 -9.6**

Chronic disease 49.0*** 15.0*** 4.82No hospital stay ref. ref. ref.Hospital stay 2010 only 6.33 75.4*** 21.4***Hospital stay 2011 only 101.2*** 159.9*** 96.2***Hospital stay 2010 & 2011 161.0*** 290.4*** 152.5***

SHE in 2010 0.14*** – 0.08***SHE in 2011 0.18*** – 0.10***

R2 0.14 0.08 0.14N 87,110 87,110 87,110* p<0.1, ** p<0.05, *** p<0.01


Table 3.5 – Empirical mean, standard deviation and percentiles of supplementary healthcareexpenditures (SHE) by risk groups λ

SHE N Mean s.d min p1 p5 p50 p95 p99 max

λ1 21,778 333 429 0 0 6 207 1016 1938 9280λ2 21,777 556 660 0 0 20 368 1626 3257 11190λ3 21,778 762 871 0 0 67 522 2195 4447 15905λ4 21,777 1215 1263 0 38 149 866 3497 6460 16681

Table 3.6 – Empirical mean, standard deviation and percentiles of OOP payments by riskgroups λ

OOP N Mean s.d min p1 p5 p50 p95 p99 max

λ1 21,778 118 219 0 0 0 48 457 1003 6820λ2 21,777 211 355 0 0 2 92 774 1715 6997λ3 21,778 298 509 0 0 12 140 1058 2404 13634λ4 21,777 498 790 0 4.5 31 250 1791 3867 13960

166 Chapter3

Figure 3.6 – Empirical distribution function of supplementary healthcare expenditures (SHE),by risk groups


Table 3.7 – Adverse-selection spiral when insurance is voluntary: effect on premiums, resultsfrom simulations

Annual Mean Min Max Low High Low High Under Overpremium (in e) risk risk income income 45 y.o. 65 y.o.

Uniform

Mandatory 523 523 523 523 523 523 523 523 523Voluntary 712 712 712 712 712 712 712 712 712Age-based

Mandatory 523 286 767 349 658 571 509 311 697Voluntary 553 286 803 361 697 604 543 311 742Medical underwriting

Mandatory 523 188 1110 325 700 562 496 311 697Voluntary 527 188 1110 293 700 566 505 308 704Experience rating

Mandatory 523 150 8086 287 821 562 496 311 697Voluntary 523 150 1642 276 808 562 494 309 689Income-based

Mandatory 523 209 1025 531 498 307 744 518 467Voluntary 795 317 1558 807 756 467 1131 788 711Income/age-based

Mandatory 523 172 1074 485 535 315 733 496 518Voluntary 735 242 1511 681 752 443 1031 659 728

168 Chapter3

Table 3.8 – Characteristics of insured and uninsured when SHI is voluntary, results fromsimulations

Sample Women Age Low Average High Chronic SHEincome income income Disease

N % % mean % % % % mean

All sample 87,110 100 65 57 21 55 24 19.6 717Uniform

Uninsured 44,021 50.5 58 47 19 56 25 8 448Insured 43,089 49.5 73 67 23 54 23 32 991Age-based

Uninsured 9,258 10.6 26 60 35 40 25 13.5 438Insured 77,852 89.4 70 57 19 57 24 20 750Medical underwriting

Uninsured 9,065 10.4 30 56 26 50 24 14 413Insured 78,045 89.6 69 57 21 55 24 20 946Experience rating

Uninsured 3,136 3.6 42 53 32 58 10 10 571Insured 83,974 96.4 66 57 21 55 24 20 722Income-based

Uninsured 44,126 50.6 57 47 10 56 35 7 465Insured 42,984 49.4 74 67 33 54 13 32 974Income/age-based

Uninsured 41,263 47.4 55 48 8 57 35 7 459Insured 45,847 52.6 75 66 33 53 14 31 948


Table 3.9 – Percentage of uninsured by income and risk profile, for each regime of premiums- results from simulations

Uniform Age-based Medical Experience Income-based Income-ageunderwriting rating based

UNINSURED % % % % % %

Whole sample 50.5 10.6 10.4 3.6 50.6 47.4

Low income 45.4 17.6 12.6 5.5 22.9 18.2Average income 51.5 7.7 9.5 3.8 51.5 49.2High income 52.8 11.2 10.7 1.5 73.2 69.0

Low risk:λ1,λ2 100 18.6 19.7 6 91.5 86.9High risk:λ3,λ4 1.1 2.6 1.1 1.2 9.8 7.8

High risk (λ3,λ4)& Low income 4.4 10.8 4.4 1.6 0 0& Average income 0 0 0 0.1 0 0& High income 0 0 0 0.1 43.4 34.4

170 Chapter3

Table 3.10 – Vertical equity indexes, results from simulation - whole sample

GI GI−(P +OOP ) CI KI REI

No insurance

0.1754 0.1810 -0.0160 -0.1915 -0.0055Uniform

Mandatory 0.1754 0.1805 0.0014 -0.1740 -0.0051Voluntary 0.1754 0.1810 -0.0162 -0.1916 -0.0056Age-based

Mandatory 0.1754 0.1811 -0.0179 -0.1933 -0.0057Voluntary 0.1754 0.1810 -0.0125 -0.1879 -0.0055Medical Underwriting

Mandatory 0.1754 0.1812 -0.0206 -0.1960 -0.0058Voluntary 0.1754 0.1810 -0.0194 -0.1949 -0.0056Experience rating

Mandatory 0.1754 0.1812 -0.0195 -0.1949 -0.0058Voluntary 0.1754 0.1811 -0.0183 -0.1938 -0.0057Income-based

Mandatory 0.1754 0.1774 0.1154 -0.0600 -0.0020Voluntary 0.1754 0.1797 0.0331 -0.1423 -0.0043Income/age-based

Mandatory 0.1754 0.1775 0.1098 -0.0657 -0.0021Voluntary 0.1754 0.1797 0.0332 -0.1422 -0.0043


Figure 3.7 – Healthcare payments and vertical equity

172 Chapter3

Table 3.11 – Risk sharing indexes, results from simulation - whole sample

GSHE GP +OOP CR KR RER

No insurance

0.5435 0.5435 0.5435 0 0Uniform

Mandatory 0.5435 0.2304 0.2145 -0.3290 0.3131Voluntary 0.5435 0.4197 0.3761 -0.1674 0.1238Age-based

Mandatory 0.5435 0.2926 0.2466 -0.2969 0.2509Voluntary 0.5435 0.3335 0.2839 -0.2596 0.2096Medical Underwriting

Mandatory 0.5435 0.3042 0.2556 -0.2879 0.2393Voluntary 0.5435 0.3421 0.2916 -0.2519 0.2014Experience rating

Mandatory 0.5435 0.3340 0.2854 -0.2581 0.2095Voluntary 0.5435 0.3411 0.2931 -0.2504 0.2024Income-based

Mandatory 0.5435 0.2744 0.2099 -0.3336 0.2690Voluntary 0.5435 0.4416 0.3818 -0.1617 0.1019Income/age-based

Mandatory 0.5435 0.2803 0.2194 -0.3241 0.2632Voluntary 0.5435 0.4341 0.3735 -0.1700 0.1094


Figure 3.8 – Healthcare payments and risk sharing

174 Chapter3

Table 3.12 – Vertical equity and Risk sharing indexes, results from simulation - SHIR only -Voluntary whole sample

CI KI REI CR KR RER

No insurance

-0.0294 -0.2048 -0.0033 0.5214 0 0Uniform

Voluntary -0.0278 -0.2032 -0.0035 0.2450 -0.2764 0.1948Age-based

Voluntary -0.0214 -0.1969 -0.0035 0.1054 -0.4161 0.2966Medical Underwriting

Voluntary -0.0326 -0.2081 -0.0036 0.1097 -0.4117 0.2840Experience rating

Voluntary -0.0305 -0.2059 -0.0037 0.1175 -0.4039 0.2834Income-based

Voluntary 0.0498 -0.1256 -0.0022 0.2531 -0.2683 0.1274Income/age-based

Voluntary 0.0498 -0.1256 -0.0022 0.2403 -0.2811 0.1380


Table 3.13 – Different values of load factor and risk aversion - Voluntary whole sample

% uninsured REI RER

Load factor = 1.1

Uniform 25.6 -0.0050 0.2035Age-based 9.7 -0.0053 0.2061Medical underwriting 5.7 -0.0053 0.2094Experience rating 0.9 -0.0054 0.2002Income-based 45.4 -0.0038 0.1150Income/age-based 42.9 -0.0039 0.1194Load factor = 1.15

Uniform 50.5 -0.0055 0.1231Age-based 9.7 -0.0055 0.2103Medical underwriting 8.1 -0.00545 0.2058Experience rating 1.9 -0.0056 0.2024Income-based 48.6 -0.0041 0.1073Income/age-based 45.2 -0.0041 0.1147Risk aversion = 0.0004

Uniform 52.8 -0.0054 0.1163Age-based 31.8 -0.0055 0.1420Medical underwriting 18.9 -0.0054 0.1709Experience rating 6.6 -0.0057 0.1971Income-based 73.5 -0.0055 0.0500Income/age-based 72.1 -0.0054 0.0520Risk aversion = 0.0006

Uniform 25.6 -0.0053 0.2100Age-based 6.8 -0.0056 0.2283Medical underwriting 6.6 -0.0058 0.2166Experience rating 1.4 -0.0057 0.2067Income-based 39.0 -0.0036 0.1324Income/age-based 35.3 -0.0037 0.1412

176 Chapter3

Appendix

A-3.1. Equity indexes: formulas and computation

Gini coefficient

The Gini coefficient is defined as twice the area between the Lorenz curve L, which plots the

cumulative income (or SHE) against the cumulative population ranked by income (or SHE). A

Gini coefficient of 0 expresses perfect equality, that is everyone has the same income (or SHE).

A Gini coefficient superior to 0 implies an unequal distribution; the closer the Gini coefficient

is to 1, the more unequal the distribution. Formally, the Gini coefficient is defined as

G = 1 − 2∫ 1

0L(p)dp (3.4)

For computation, we use the covariance approach derived in Pyatt et al. (1980)

G =2µ

cov(y,r) (3.5)

where y is the income (or SHE), µ its mean and r the fractional rank, ranging all individuals

according to their income (or SHE) from the poorest to richest (from the lowest to the highest

healthcare user). The weighted fractional rank is indeed defined as

ri =i−1∑

j=0

wj +wi

2(3.6)

where wi is the sample weight scaled to sum 1. Observations are sorted in ascending order of

income (or SHE) and w0 = 0.

Concentration index

The concentration index is defined as twice the area between the concentration curve LP +OOP ,

that plots the cumulative healthcare payments against the cumulative population ranked by

Appendix 177

income (or SHE). The concentration index is bounded between -1 and 1. Formally, the concen-

tration index is defined as

C = 1 − 2∫ 1

0LP +OOP (p)dp (3.7)

For computation, we use the covariance approach described in Jenkins (1988),

C =2µ

cov((P + OOP ),r) (3.8)

where P + OOP is the healthcare payments, µ its mean and r the fractional rank in the income

(or SHE) distribution, as defined previously in equation 3.6.

Kakwani index

One way to measure the progressivity of payments, i.e. ‘comparing the share of income received

by each income decile with its share of health care payments’ (Wagstaff & Van Doorslaer 2000),

is to use the Kakwani index (Kakwani 1977). The Kakwani index is defined as twice the area

between the Lorenz curve of income (or SHE), LI(p), and the concentration curve of health care

payments LP +OOP . The Kakwani index is therefore the difference between the concentration

index for healthcare payments and the Gini coefficient for income (or SHE):

K = C − G (3.9)

If the system is progressive, K is positive. It the system is regressive, K is negative. If payments

are perfectly proportional to income (or SHE), then K = 0.

Redistribution index

The measure of the redistributive impact of healthcare payments, either on income or SHE

distribution, can be measured by comparing the Gini coefficients before and after healthcare

payments. Formally, if we focus on income distribution,

178 Chapter3

REI = GI − GI−(P +OOP ) (3.10)

where GI is the Gini coefficient for income before any healthcare payments and GI−(P +OOP ),

the Gini coefficients once individuals have paid their insurance premium and OOP payments.

If we focus on risk sharing then,

RER = GSHE − GP +OOP (3.11)

where GSHE is the Gini coefficient for SHE and GP +OOP , the Gini coefficients of healthcare

payments.

Stata code

We provide here the Stata code used to compute the different indexes14. y represents the indi-

vidual income before any healthcare payment, she the supplementary healthcare expenditures.

hp are the healthcare payments borne by the individuals, that is the premium (if the individual

is insured) plus OOP payments. For each regime x, and depending on whether SHI is voluntary

or mandatory, we use the corresponding hp for each individual, obtained from the simulation. r

is the fractional rank, computed as in equation 3.6. The Gini coefficient and the concentration

index are computed respectively as in equations 3.5 and 3.8.

14The Stata code is derived from the one provided by the World Bank technical doc-uments available on http://siteresources.worldbank.org/INTPAH/Resources/Publications/459843-1195594469249/HealthEquityCh8.pdf

Appendix 179

Figure 3.9 – Stata code - vertical equity indexes

Figure 3.10 – Stata code - risk sharing indexes

180 Chapter3

A-3.2. Simulation

We import from Stata the empirical distribution of SHE and OOP payments estimated on our

sample and use Excel to compute individuals’ expected utility with and without insurance. We

use the Simpson’s rule (with quadratic interpolation) to approximate the integral. The decision

to take out SHI is simulated thanks to a VBA macro, written by the author. We first compute

the premium paid by the individual and her expected utility with insurance. If the expected

utility with insurance is higher than without, the individual takes out insurance and remains

in the pool. If not he exits the pool. When the premium depends on the pool (uniform, age-

based, income and income-age based), we compute the premium again and repeat the steps

until we reach an equilibrium, that is the pool after iteration j is the same than for iteration

j − 1. Eventually, for each individual in our sample we get the premium he would have to pay,

her expected utility considering this premium and her decision to remain insured or exit the

pool. The last iteration identifies individuals who take out SHI and those who prefer to remain

uninsured. We also compute the final premium paid by those who want to be insured, taking

into account the equilibrium pool. Finally, results are exported to Stata to run the analyses

and compute the vertical equity and risk sharing indexes. The Excel macro is coded using

VBA language. We provide the code used to compute the expected utility as well as uniform

premiums when insurance is voluntary. The macros for the other type of premiums as well as

detailed simulation results are available on demand.

Appendix 181

Figure 3.11 – Macro for computing expected utilities

182 Chapter3

Figure 3.12 – Macro for simulating adverse selection with uniform premiums

General Conclusion

The purpose of this thesis was to deal with two questions relative to efficiency and fairness in

mixed health insurance systems with partial mandatory coverage and voluntary supplementary

health insurance (SHI): (i) the potential inflationary effect of SHI on medical prices; (ii) the

fairness of SHI premiums in a context of voluntary insurance.

Main results

Does SHI encourage the rise in medical prices?

We find that generous supplementary coverage can contribute to a rise in medical prices by

increasing the demand for specialists who balance bill. Individuals with better coverage raise

their proportion of consultations of specialists who balance bill by 9%, which results in a 32%

increase in the amount of balance billing per consultation. In addition to moral hazard on qual-

ity of care, we also find for some patients evidence of an increase in the number of specialists

consultations due to better coverage, which suggests that balance billing limited their access

to specialists. However, the magnitude of moral hazard clearly depends on supply side orga-

nization. We find no evidence of moral hazard, neither in quantity nor quality, in areas where

physicians who charge the regulated fee are widely available. In other words, when patients

can readily choose between physicians who balance bill and physicians who don’t, SHI has no

impact on medical prices. On the basis of these results, it seems that the most appropriate

policy to contain medical prices is not to limit SHI coverage but to monitor the supply of care

in order to guarantee patients a genuine choice of their physicians.

Is there evidence of selection on moral hazard in SHI?

184 General Conclusion



ask for comprehensive SHI are also those who exhibit stronger moral hazard, i. e. a larger in-

crease in balance billing per consultation. We also find that individuals’ income is a determinant

of balance billing consumption and influences the behavioral response to better coverage. With-

out coverage, the poor consume less balance billing than the rich but increase more strongly

their balance billing consumption if they benefit from better coverage. They are also more likely

to ask for comprehensive coverage. In a context where SHI is voluntary, the inflationary impact

of SHI coverage might be worsened by selection on moral hazard. When providing compre-

hensive balance billing coverage, insurers have to take into account that their contract is likely

to attract individuals who respond more sharply than average to better coverage. Our policy

conclusions as regards the role of income are of different nature. The negative effect of income

on the demand for consultations with balance billing coupled with its positive effect on moral

hazard reveals that insurance plays an important role in terms of access to care.

Are SHI age-based premiums fair?

Our simulations show that when SHI is voluntary, age-based premiums allow the largest transfers

from low to high healthcare users. Indeed, age-based premiums are a cross-breed between CR

and actuarial fairness: they better resist to the adverse selection spiral than uniform or income-

based premiums and still guarantee more risk sharing than medical underwriting or experience

rating. In addition, we stress out the fact that voluntary insurance dramatically limits the

impact of SHI on risk sharing and vertical equity, especially when premiums are based on a form

of community rating. Finally, we show that there is a conflict between disconnecting healthcare

expenditures from healthcare payments and guaranteeing vertical equity. Indeed, although age-

based premiums imply a form of risk sharing especially when insurance is voluntary, they also

yield regressive payments and raise legitimate concerns about the affordability of insurance and

income inequalities due to healthcare payments.


Limitations

Our database provides valuable information and a useful design to explore the effect of SHI on

medical consumption. Our empirical strategy is meant to control for endogeneous selection and

estimates are robust to different specifications. However this work suffers from some limita-

tions. First, our sample is not representative of the French population nor of individuals likely

to buy SHI in the market. Because they are mainly teachers and Ministry of education em-

ployees, MGEN policyholders have specific observable characteristics. Compared to the general

population, our sample has significantly more women, average age as well as median wage are

higher. As regards unobservable characteristics, we cannot rule out the possibility that MGEN

policyholders are also different in terms of risk aversion, health preferences or moral hazard

behavior. One of the important finding of this thesis is that individual heterogeneity in the de-

mand for healthcare and response to better coverage is significant and plays a critical role in the

demand for insurance coverage. Generalizing our results to a different setting and population

would therefore require strong assumptions. However, estimating marginal treatment effects

is a first step in acknowledging individual heterogeneity and evaluate how it impacts selection

and moral hazard. Theoretically, we should be able to reconstruct policy relevant parameters

from MTEs, and estimating the effect of SHI on balance billing consumption for any specific

population. However our common support is too restricted at this point to go further. Another

limitation of our data is that we do not have precise information about switchers’ new coverage.

Because MGEN does not cover balance billing, we know that switchers’ balance billing coverage

will be equal or higher and are therefore able to provide lower-bound estimates of SHI impact.

However, we are not able to refine the analysis and estimate price elasticities without making

further assumptions.

Our investigation on the impact of age-based premiums on risk sharing and vertical equity is

still at an exploratory stage. Several methodological choices and assumptions we made are

questionable although often dictated by data availability. We believe that a micro-simulation is

relevant to answer this type of question. However, the predictive power of our model could be

improved with more precise data. With the data currently available, we have to make strong

assumptions about individuals’ risk aversion and our model for health insurance demand is


not as refined as we wish it would be. Moreover, our analysis is restricted to the SHI benefit

package because we are not able to observe in details hospital expenditures which are mainly

covered by NHI. For the same reasons, we also probably underestimate the magnitude and

dispersion of OOP expenditures. A last limitation of this work comes from our pragmatic

definition of fairness. Restricting our analysis to healthcare financing, through the spectra

of risk sharing and vertical equity, only partially answers the fairness question. A broader

vision including healthcare consumption, net income and health would be far more satisfying.

However this would require individual-level data that combine comprehensive information on

health, healthcare use, net income as well as coverage choices and healthcare payments.

Policy relevance

Although we acknowledge the limitations of our results, we believe this thesis can contribute to

critical policy debates as regards future evolutions of SHI in France and more generally in mixed

health insurance systems. The definition of the benefit package and the articulation between

NHI and SHI is a major policy question and will underly forthcoming reforms of social health

insurance systems. The question of a mandatory SHI also regularly comes back in the public

debate.

Should SHI coverage on balance billing be limited?

We have already emphasized the continuous increase of balance billing in France and the burden

it causes to patients in terms of OOP payments and access to care. Two measures have been

recently implemented by the French government to deal with balance billing. One consists in

giving financial incentives to physicians for limiting consultation fees. The other one consists

in giving incentives to insurers for limiting balance billing coverage. Physicians are invited to

sign up a NHI agreement called ‘Contrat d’acces aux soins’ (CAS). This agreement is meant

to discourage physicians to charge balance billing in exchange of fiscal advantages and a better

remuneration of some clinical and technical acts. Note that the balance billing limit is quite

flexible and not extremely restrictive since physicians only commit to charge fees, on average,

up to 100% of the NHI reference fee. Is the CAS able to monitor the supply side and limit the


inflationary spiral between SHI and balance billing? First, the CAS does not encounter a great

success: according to physician unions, less than a third of all practitioners has actually signed

the agreement. Moreover, the CAS does not deal with what we identified as the main driver

of the inflationary spiral: the scarcity of S1 physicians in some areas. We argue that it also

increases complexity and uncertainty in the way specialists set their fees. The CAS agreement

states that physicians must provide a given share of their consultations with the reference fee. It

means that for some patients (which patients?) physicians are allowed to charge balance billing

far above the 100% ‘average limit’. This increases uncertainty for patients as regards their

OOP expenditures. Inciting physicians to price discriminate their patients also raises ethical

questions as regards equal access to care.

If the supply side cannot be monitored, limiting SHI coverage could be a second-best solution.

Most of the SHI contracts provided on the individual and the employer-based markets are

certified as ‘Contrats responsables’. In order to benefit from fiscal advantages, insurers have to

meet certain standards in terms of level of coverage and premiums. Since April 2015 the French

government has included a limitation in balance billing coverage15. The rule is quite complex

because it depends on whether the physician is part of the ‘CAS’ agreement or not. Basically,

there is no limit in balance billing coverage if the physician signed up for CAS. However, the

coverage is limited to 100% of the NHI reference fee if the physician did not sign up. On the

basis of our results, we are sceptical about the efficiency of this measure. First, it assumes that

patients are not only able to freely choose between S1 and S2 physicians but also to distinguish,

among S2 physicians, between those who are part of the CAS agreement and those who are not.

We also show that demand for S2 specialists is heavily constrained by S1 availability and that

SHI actually enhances access to care for individuals with low income and/or living in areas with

very few S1 specialists. We can therefore expect two consequences of limiting coverage in areas

where S1 specialists are scarce: either an increase in OOP expenditures or mounting difficulties

in visiting specialists for those who cannot afford balance billing.

Should the SHI perimeter expand?

15Décret n° 2014-1374 du 18 novembre 2014 relatif au contenu des contrats d’assurance maladie complémentairebénéficiant d’aides fiscales et sociales


The right-wing candidate for the forthcoming French presidential election, Francois Fillon, ex-

plicitly considers SHI expansion as the answer to NHI deficit. According to Mr Fillon, universal

and mandatory NHI should only cover ‘serious’ or chronic diseases and let SHI cover, well, ba-

sically everything else16. To be fair, since the beginning of the 90’s, the successive governments,

irrespective of their political affiliation, have been keen to support SHI expansion in order to

release the constraints on public finance. The idea of limiting public coverage to catastrophic

expenditures and let individuals decide whether they want to be covered against ‘small risks’ is

not new either. However, SHI expansion cannot be considered as a simple and harmless transfer

from public to private finance of healthcare. This will necessarily have important consequences

on inequalities in coverage and premium paid and will affect the extent of risk sharing and ver-

tical equity. First, our results on SHI reimbursements and OOP expenditures distribution show

that there is no such things as ‘small risks’. Indeed, the risk can not be assessed by looking at

average expenditures, one has to consider the whole distribution and especially the highest per-

centiles. Although the average OOP expenditures after NHI reimbursement is approximatively

e436 in our sample, it exceeds e1350 for 5% of individuals. SHI expansion will probably yield

wider dispersion of expenditures meant to be covered by SHI, and transform the apparent ‘small

risk’ in a substantial one. Second, we also show that SHI reimbursements are already highly

correlated with individual characteristics, and especially with age. Increasing SHI perimeter

would necessarily increase heterogeneity in terms of healthcare risk faced by individuals and

consequently increase inequalities in premiums and out-of-pocket expenditures. Finally, we can

expect adverse selection phenomenons to be worsened by the wider gap between low and high

risks.

Should SHI coverage be mandatory?

Guaranteeing access to a SHI contract has been set as a priority objective by the French gov-

ernment since 2012. The main resolution consisted in making SHI coverage mandatory for all

employees, through an employer-based contracts17. However, for those who are not employees

16"Pour assurer la pérennité de notre système de santé je propose de [...] focaliser l’assurancepublique universelle sur des affections graves ou de longue durée, et l’assurance privée sur le reste" inhttps://www.fillon2017.fr/participez/sante

17The agreement is part of the Accord National Interprofessionnel It was signed by unions in January 2013and implemented in January 2016


with long-term contracts, such as students, employees under short-term contracts, independent

workers, civil servants, unemployed or retirees, SHI is still voluntary. What if SHI was also

mandatory in the individual market?

The impact of a mandatory SHI would not be limited to the coverage of the currently uninsured

population, which is quite marginal (only 5%). It could also have important benefits in terms

of risk sharing and vertical equity. We showed in Chapter 3 that when insurance is mandatory,

uniform or income-based premiums allow for higher transfers between low and high healthcare

users as well as between low and high income. This would also reduce inequalities between

insiders, who benefit from mandatory employer-based contracts, and outsiders (young and old

people, working-poor, unemployed) who face higher premiums on the individual market. Would

a mandatory SHI yield a rise in prices due to moral hazard? It would indeed create an increase

in coverage for the 5% of the population which is not currently covered. However, this increase

in healthcare consumption can be desirable for low-income individuals who could not access

SHI before. Furthermore, given the evidence of selection on moral hazard, we can also expect

that individuals who prefer to remain uninsured would not strongly increase their consumption

with better coverage. It is true however that for individuals who are better off without SHI, a

mandate would force them to over-consume health insurance .

Future research

We plan to pursue our research in three directions. Two of our projects continue to investigate

the role of SHI in healthcare use and its articulation with NHI. The third project builds a bridge

between the methods used in the thesis and specific challenges we face in Health technology

assessment (HTA) studies.

We want to explore further the demand for SHI and its impact on healthcare use. Besides

balance billing, optical and dental care are also of interest. Indeed, SHI coverage varies signifi-

cantly on optical and dental care, prices keep on increasing and studies report important access

inequalities. Up to now, we were limited by partial information on switchers’ new coverage.

This was sufficient to estimate moral hazard on balance billing but too limited to evaluate the


impact of SHI on optical and dental care. Furthermore, with precise information on level of

coverage, we should be able to derive price elasticities and estimate welfare impacts. Hopefully,

we may be able to ‘upgrade’ our database. Indeed, whereas the MGEN-SHI contract was iden-

tical for every policyholders, MGEN now offers new SHI contracts with three different levels of

coverage. Individuals can ask for better coverage on balance billing as well as on optical and

dental care. This change in MGEN’s offer potentially represents an incredible source of data to

investigate the demand for SHI and the response to a change in coverage.

Our second project focuses on the articulation NHI/SHI. There are two questions we want to

investigate: (i) Does SHI cancel out the solidarity implied by the NHI?; (ii) What would be the

distributional impact of a change in NHI benefit package? Following the same methodology than

for SHI premiums, we want to estimate the impact of NHI on risk sharing and vertical equity. We

could then compare the distributional impact of NHI with SHI to reveal potential contradictory

effects. We could also simulate the impact of a change in the NHI benefit package. For instance,

if ambulatory care were only covered by SHI, how would it impact transfers between low and

high healthcare users and between low and high income groups? To answer these questions,

one of the main challenges lies in collecting appropriate data with comprehensive information

on NHI and SHI reimbursements.

Our third project is methodological and focuses on the opportunity to apply Marginal Treatment

Effect to HTA work. The effectiveness of a new treatment is usually assessed based on the results

of a randomized trial. A randomized group of patients receive the standard treatment (control

group) while others receive the new treatment (treatment group). The outcome difference

between the two groups (survival rate for instance) gives the average treatment effect (ATE).

However, mainly for ethical reasons, patients from the control group are sometimes allowed to

also receive the new treatment. This ‘crossover’ introduces possible endogeneous selection and

requires specific methods to estimate an unbiased average treatment effect (ATE). The methods

commonly used are actually very close to matching or IV approaches and consequently rely on

the same key assumption: the treatment effect is supposed to be homogeneous across patients.

Yet, this might not be the case if patients are selected or select themselves according to their

expected response to treatment. To deal with crossover issues, testing for essential heterogeneity


and applying MTE could therefore be appropriate. Basu et al. (2007) give evidence of essential

heterogeneity in the choice for breast cancer treatments and stress out its impact on cost-

effectiveness. However, there is a methodological challenge in applying MTE to trial data.

Indeed, data available often includes small samples and limited covariates. The methodology

developed by Brinch et al. (2012) and used by Kowalski (2015) in a context of randomized

experiments could be an interesting starting point.

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Résumé

Mots Clés

Abstract

Keywords

Cette thèse est consacrée aux systèmesd’assurance maladie mixtes où la couverturepublique obligatoire peut être complétée par uneassurance privée (complémentaire santé). Lesquestions abordées portent sur l’effetinflationniste de la complémentaire santé sur leprix des soins et sur l’impact de la tarification àl’âge sur les solidarités entre malades et bienportants et entre catégories de revenu.

Les analyses empiriques sont réalisées surdonnées françaises. Cette base de donnéesoriginale regroupe les consommations de soinsde 99,878 affiliés à la MGEN sur la période2010-2012.

Le chapitre 1 estime l’effet causal d’unecouverture complémentaire généreuse sur laconsommation de dépassements d’honoraires.Une meilleure couverture augmente la demandepour les spécialistes qui pratiquent desdépassements d’honoraires, ce qui contribue àl’augmentation du prix des soins. Toutefois, ceteffet inflationniste ne concerne que lesdépartements où l’accès aux spécialistes estlimité. Le modèle développé dans le chapitre 2tient compte du fait que l'impact d'une meilleurecouverture sur les dépassements (aléa moral)varie d'un individu à l'autre et que cettehétérogénéité peut être corrélée à la demanded’assurance. De fait, l’effet inflationniste de lacomplémentaire est accentué par des effets desélection : les assurés qui recherchent unemeilleure couverture sont aussi ceux quimontrent le plus d’aléa moral. L’impact de lacouverture est également plus fort pour les basrevenus. Dans le chapitre 3, nous utilisons lesdonnées MGEN pour simuler l’impact de latarification à l’âge sur les niveaux de primes et ladécision de s’assurer en prenant en compte lescorrélations entre âge, état de santé et revenu.Quand l'assurance n'est pas obligatoire, latarification à l’âge permet de maximiser lestransferts entre malades et bien portants audétriment toutefois de la solidarité entre hauts etbas revenus.

This thesis deals with two questions relativeto efficiency and fairness in mixed healthinsurance systems with partial mandatorycoverage and voluntary supplementary healthinsurance (SHI): (i) the potential inflationaryeffect of SHI on medical prices; (ii) the fairnessof SHI premiums in a context of voluntaryinsurance.

We set the analysis in the French context andperform empirical analyses on originalindividual-level data, collected from theadministrative claims of a French insurer(MGEN). The sample is made of 99,878individuals observed from 2010 to 2012.

In Chapter 1, we estimate the causal impactof a generous SHI on patients’ decisions toconsult physicians who balance bill, i.e. chargemore than the regulated fee. We find evidencethat better coverage increases demand forconsultations with balance billing, therebycontributing to the rise in medical prices.However, the impact is not significant whenindividuals have a real choice between types ofphysicians. In Chapter 2, we specify individualheterogeneity in moral hazard and consider itspossible correlation with coverage choices(essential heterogeneity). We find evidence ofselection on moral hazard: individuals who aremore likely to ask for comprehensive SHI exhibita larger increase in balance billing perconsultation. The impact of better coverage islarger for low income people, suggesting thatinsurance plays a role in access to care. InChapter 3, we use MGEN data to simulate theimpact of age-based premiums on the level ofpremiums and on subscription to SHI. We takeinto account effective correlations between age,health state and income. Simulation resultsshow that in a context of voluntary SHI,age-based premiums maximize transfersbetween low and high healthcare users but donot guarantee vertical equity.

Assurance maladie ; Complémentaire santé ;Aléa moral ; Anti-sélection ; Dépassementsd’honoraires ; Tarification à l’âge

Health insurance; Supplementary healthinsurance; Moral hazard; Adverse selection;Balance billing; Age-based premiums

three essays on supplementary health insurance

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